Commit | Line | Data |
---|---|---|
13a12e00 JH |
1 | package Math::BigInt; |
2 | ||
3 | # | |
4 | # "Mike had an infinite amount to do and a negative amount of time in which | |
5 | # to do it." - Before and After | |
6 | # | |
7 | ||
58cde26e | 8 | # The following hash values are used: |
0716bf9b | 9 | # value: unsigned int with actual value (as a Math::BigInt::Calc or similiar) |
58cde26e JH |
10 | # sign : +,-,NaN,+inf,-inf |
11 | # _a : accuracy | |
12 | # _p : precision | |
0716bf9b | 13 | # _f : flags, used by MBF to flag parts of a float as untouchable |
b4f14daa | 14 | |
574bacfe JH |
15 | # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since |
16 | # underlying lib might change the reference! | |
17 | ||
58cde26e | 18 | my $class = "Math::BigInt"; |
0716bf9b | 19 | require 5.005; |
58cde26e | 20 | |
2d2b2744 | 21 | $VERSION = '1.73'; |
58cde26e JH |
22 | use Exporter; |
23 | @ISA = qw( Exporter ); | |
091c87b1 | 24 | @EXPORT_OK = qw( objectify bgcd blcm); |
b282a552 T |
25 | # _trap_inf and _trap_nan are internal and should never be accessed from the |
26 | # outside | |
27 | use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode | |
28 | $upgrade $downgrade $_trap_nan $_trap_inf/; | |
58cde26e JH |
29 | use strict; |
30 | ||
31 | # Inside overload, the first arg is always an object. If the original code had | |
091c87b1 T |
32 | # it reversed (like $x = 2 * $y), then the third paramater is true. |
33 | # In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes | |
34 | # no difference, but in some cases it does. | |
58cde26e JH |
35 | |
36 | # For overloaded ops with only one argument we simple use $_[0]->copy() to | |
37 | # preserve the argument. | |
38 | ||
39 | # Thus inheritance of overload operators becomes possible and transparent for | |
40 | # our subclasses without the need to repeat the entire overload section there. | |
a0d0e21e | 41 | |
a5f75d66 | 42 | use overload |
58cde26e JH |
43 | '=' => sub { $_[0]->copy(); }, |
44 | ||
58cde26e JH |
45 | # some shortcuts for speed (assumes that reversed order of arguments is routed |
46 | # to normal '+' and we thus can always modify first arg. If this is changed, | |
47 | # this breaks and must be adjusted.) | |
48 | '+=' => sub { $_[0]->badd($_[1]); }, | |
49 | '-=' => sub { $_[0]->bsub($_[1]); }, | |
50 | '*=' => sub { $_[0]->bmul($_[1]); }, | |
51 | '/=' => sub { scalar $_[0]->bdiv($_[1]); }, | |
027dc388 JH |
52 | '%=' => sub { $_[0]->bmod($_[1]); }, |
53 | '^=' => sub { $_[0]->bxor($_[1]); }, | |
54 | '&=' => sub { $_[0]->band($_[1]); }, | |
55 | '|=' => sub { $_[0]->bior($_[1]); }, | |
58cde26e JH |
56 | '**=' => sub { $_[0]->bpow($_[1]); }, |
57 | ||
2d2b2744 T |
58 | '<<=' => sub { $_[0]->blsft($_[1]); }, |
59 | '>>=' => sub { $_[0]->brsft($_[1]); }, | |
60 | ||
b3abae2a | 61 | # not supported by Perl yet |
027dc388 JH |
62 | '..' => \&_pointpoint, |
63 | ||
58cde26e | 64 | '<=>' => sub { $_[2] ? |
bd05a461 | 65 | ref($_[0])->bcmp($_[1],$_[0]) : |
f9a08e12 | 66 | $_[0]->bcmp($_[1])}, |
027dc388 | 67 | 'cmp' => sub { |
58cde26e | 68 | $_[2] ? |
b3abae2a JH |
69 | "$_[1]" cmp $_[0]->bstr() : |
70 | $_[0]->bstr() cmp "$_[1]" }, | |
58cde26e | 71 | |
091c87b1 T |
72 | # make cos()/sin()/exp() "work" with BigInt's or subclasses |
73 | 'cos' => sub { cos($_[0]->numify()) }, | |
74 | 'sin' => sub { sin($_[0]->numify()) }, | |
75 | 'exp' => sub { exp($_[0]->numify()) }, | |
76 | 'atan2' => sub { atan2($_[0]->numify(),$_[1]) }, | |
77 | ||
78 | 'log' => sub { $_[0]->copy()->blog($_[1]); }, | |
58cde26e JH |
79 | 'int' => sub { $_[0]->copy(); }, |
80 | 'neg' => sub { $_[0]->copy()->bneg(); }, | |
81 | 'abs' => sub { $_[0]->copy()->babs(); }, | |
b3abae2a | 82 | 'sqrt' => sub { $_[0]->copy()->bsqrt(); }, |
58cde26e JH |
83 | '~' => sub { $_[0]->copy()->bnot(); }, |
84 | ||
12fc2493 | 85 | # for subtract it's a bit tricky to not modify b: b-a => -a+b |
091c87b1 | 86 | '-' => sub { my $c = $_[0]->copy; $_[2] ? |
12fc2493 | 87 | $c->bneg()->badd( $_[1]) : |
091c87b1 T |
88 | $c->bsub( $_[1]) }, |
89 | '+' => sub { $_[0]->copy()->badd($_[1]); }, | |
90 | '*' => sub { $_[0]->copy()->bmul($_[1]); }, | |
91 | ||
92 | '/' => sub { | |
93 | $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]); | |
94 | }, | |
95 | '%' => sub { | |
96 | $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]); | |
97 | }, | |
98 | '**' => sub { | |
99 | $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]); | |
100 | }, | |
101 | '<<' => sub { | |
102 | $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]); | |
103 | }, | |
104 | '>>' => sub { | |
105 | $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]); | |
106 | }, | |
107 | '&' => sub { | |
108 | $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]); | |
109 | }, | |
110 | '|' => sub { | |
111 | $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]); | |
112 | }, | |
113 | '^' => sub { | |
114 | $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]); | |
115 | }, | |
116 | ||
117 | # can modify arg of ++ and --, so avoid a copy() for speed, but don't | |
118 | # use $_[0]->bone(), it would modify $_[0] to be 1! | |
58cde26e JH |
119 | '++' => sub { $_[0]->binc() }, |
120 | '--' => sub { $_[0]->bdec() }, | |
121 | ||
122 | # if overloaded, O(1) instead of O(N) and twice as fast for small numbers | |
123 | 'bool' => sub { | |
124 | # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/ | |
091c87b1 | 125 | # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef; :-( |
3a427a11 RGS |
126 | my $t = undef; |
127 | $t = 1 if !$_[0]->is_zero(); | |
b3abae2a | 128 | $t; |
58cde26e | 129 | }, |
a0d0e21e | 130 | |
027dc388 JH |
131 | # the original qw() does not work with the TIESCALAR below, why? |
132 | # Order of arguments unsignificant | |
133 | '""' => sub { $_[0]->bstr(); }, | |
134 | '0+' => sub { $_[0]->numify(); } | |
a5f75d66 | 135 | ; |
a0d0e21e | 136 | |
58cde26e JH |
137 | ############################################################################## |
138 | # global constants, flags and accessory | |
139 | ||
990fb837 RGS |
140 | # these are public, but their usage is not recommended, use the accessor |
141 | # methods instead | |
0716bf9b | 142 | |
ee15d750 JH |
143 | $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc' |
144 | $accuracy = undef; | |
145 | $precision = undef; | |
146 | $div_scale = 40; | |
58cde26e | 147 | |
b3abae2a JH |
148 | $upgrade = undef; # default is no upgrade |
149 | $downgrade = undef; # default is no downgrade | |
150 | ||
990fb837 RGS |
151 | # these are internally, and not to be used from the outside |
152 | ||
b282a552 | 153 | sub MB_NEVER_ROUND () { 0x0001; } |
990fb837 RGS |
154 | |
155 | $_trap_nan = 0; # are NaNs ok? set w/ config() | |
156 | $_trap_inf = 0; # are infs ok? set w/ config() | |
157 | my $nan = 'NaN'; # constants for easier life | |
158 | ||
159 | my $CALC = 'Math::BigInt::Calc'; # module to do the low level math | |
091c87b1 | 160 | # default is Calc.pm |
990fb837 RGS |
161 | my $IMPORT = 0; # was import() called yet? |
162 | # used to make require work | |
9b924220 RGS |
163 | my %WARN; # warn only once for low-level libs |
164 | my %CAN; # cache for $CALC->can(...) | |
b282a552 | 165 | my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math |
b282a552 | 166 | |
027dc388 JH |
167 | ############################################################################## |
168 | # the old code had $rnd_mode, so we need to support it, too | |
169 | ||
170 | $rnd_mode = 'even'; | |
171 | sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } | |
172 | sub FETCH { return $round_mode; } | |
173 | sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } | |
174 | ||
b282a552 T |
175 | BEGIN |
176 | { | |
177 | # tie to enable $rnd_mode to work transparently | |
178 | tie $rnd_mode, 'Math::BigInt'; | |
179 | ||
180 | # set up some handy alias names | |
181 | *as_int = \&as_number; | |
182 | *is_pos = \&is_positive; | |
183 | *is_neg = \&is_negative; | |
184 | } | |
027dc388 JH |
185 | |
186 | ############################################################################## | |
187 | ||
58cde26e JH |
188 | sub round_mode |
189 | { | |
ee15d750 | 190 | no strict 'refs'; |
58cde26e | 191 | # make Class->round_mode() work |
ee15d750 JH |
192 | my $self = shift; |
193 | my $class = ref($self) || $self || __PACKAGE__; | |
58cde26e JH |
194 | if (defined $_[0]) |
195 | { | |
196 | my $m = shift; | |
990fb837 RGS |
197 | if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/) |
198 | { | |
199 | require Carp; Carp::croak ("Unknown round mode '$m'"); | |
200 | } | |
b3abae2a | 201 | return ${"${class}::round_mode"} = $m; |
58cde26e | 202 | } |
990fb837 | 203 | ${"${class}::round_mode"}; |
ee15d750 JH |
204 | } |
205 | ||
b3abae2a JH |
206 | sub upgrade |
207 | { | |
208 | no strict 'refs'; | |
28df3e88 | 209 | # make Class->upgrade() work |
b3abae2a JH |
210 | my $self = shift; |
211 | my $class = ref($self) || $self || __PACKAGE__; | |
9393ace2 JH |
212 | # need to set new value? |
213 | if (@_ > 0) | |
b3abae2a JH |
214 | { |
215 | my $u = shift; | |
216 | return ${"${class}::upgrade"} = $u; | |
217 | } | |
990fb837 | 218 | ${"${class}::upgrade"}; |
b3abae2a JH |
219 | } |
220 | ||
28df3e88 JH |
221 | sub downgrade |
222 | { | |
223 | no strict 'refs'; | |
224 | # make Class->downgrade() work | |
225 | my $self = shift; | |
226 | my $class = ref($self) || $self || __PACKAGE__; | |
9393ace2 JH |
227 | # need to set new value? |
228 | if (@_ > 0) | |
28df3e88 JH |
229 | { |
230 | my $u = shift; | |
231 | return ${"${class}::downgrade"} = $u; | |
232 | } | |
990fb837 | 233 | ${"${class}::downgrade"}; |
28df3e88 JH |
234 | } |
235 | ||
ee15d750 JH |
236 | sub div_scale |
237 | { | |
238 | no strict 'refs'; | |
990fb837 | 239 | # make Class->div_scale() work |
ee15d750 JH |
240 | my $self = shift; |
241 | my $class = ref($self) || $self || __PACKAGE__; | |
242 | if (defined $_[0]) | |
243 | { | |
990fb837 RGS |
244 | if ($_[0] < 0) |
245 | { | |
246 | require Carp; Carp::croak ('div_scale must be greater than zero'); | |
247 | } | |
ee15d750 JH |
248 | ${"${class}::div_scale"} = shift; |
249 | } | |
990fb837 | 250 | ${"${class}::div_scale"}; |
58cde26e JH |
251 | } |
252 | ||
253 | sub accuracy | |
254 | { | |
ee15d750 JH |
255 | # $x->accuracy($a); ref($x) $a |
256 | # $x->accuracy(); ref($x) | |
257 | # Class->accuracy(); class | |
258 | # Class->accuracy($a); class $a | |
58cde26e | 259 | |
ee15d750 JH |
260 | my $x = shift; |
261 | my $class = ref($x) || $x || __PACKAGE__; | |
58cde26e | 262 | |
ee15d750 JH |
263 | no strict 'refs'; |
264 | # need to set new value? | |
58cde26e JH |
265 | if (@_ > 0) |
266 | { | |
ee15d750 | 267 | my $a = shift; |
990fb837 RGS |
268 | # convert objects to scalars to avoid deep recursion. If object doesn't |
269 | # have numify(), then hopefully it will have overloading for int() and | |
270 | # boolean test without wandering into a deep recursion path... | |
271 | $a = $a->numify() if ref($a) && $a->can('numify'); | |
272 | ||
273 | if (defined $a) | |
274 | { | |
275 | # also croak on non-numerical | |
276 | if (!$a || $a <= 0) | |
277 | { | |
278 | require Carp; | |
279 | Carp::croak ('Argument to accuracy must be greater than zero'); | |
280 | } | |
281 | if (int($a) != $a) | |
282 | { | |
283 | require Carp; Carp::croak ('Argument to accuracy must be an integer'); | |
284 | } | |
285 | } | |
ee15d750 JH |
286 | if (ref($x)) |
287 | { | |
288 | # $object->accuracy() or fallback to global | |
ef9466ea T |
289 | $x->bround($a) if $a; # not for undef, 0 |
290 | $x->{_a} = $a; # set/overwrite, even if not rounded | |
291 | delete $x->{_p}; # clear P | |
990fb837 | 292 | $a = ${"${class}::accuracy"} unless defined $a; # proper return value |
ee15d750 JH |
293 | } |
294 | else | |
295 | { | |
ef9466ea T |
296 | ${"${class}::accuracy"} = $a; # set global A |
297 | ${"${class}::precision"} = undef; # clear global P | |
ee15d750 | 298 | } |
ef9466ea | 299 | return $a; # shortcut |
ee15d750 JH |
300 | } |
301 | ||
f9a08e12 JH |
302 | my $r; |
303 | # $object->accuracy() or fallback to global | |
304 | $r = $x->{_a} if ref($x); | |
305 | # but don't return global undef, when $x's accuracy is 0! | |
306 | $r = ${"${class}::accuracy"} if !defined $r; | |
307 | $r; | |
990fb837 | 308 | } |
58cde26e JH |
309 | |
310 | sub precision | |
311 | { | |
ee15d750 JH |
312 | # $x->precision($p); ref($x) $p |
313 | # $x->precision(); ref($x) | |
314 | # Class->precision(); class | |
315 | # Class->precision($p); class $p | |
58cde26e | 316 | |
ee15d750 JH |
317 | my $x = shift; |
318 | my $class = ref($x) || $x || __PACKAGE__; | |
58cde26e | 319 | |
ee15d750 | 320 | no strict 'refs'; |
58cde26e JH |
321 | if (@_ > 0) |
322 | { | |
ee15d750 | 323 | my $p = shift; |
990fb837 RGS |
324 | # convert objects to scalars to avoid deep recursion. If object doesn't |
325 | # have numify(), then hopefully it will have overloading for int() and | |
326 | # boolean test without wandering into a deep recursion path... | |
327 | $p = $p->numify() if ref($p) && $p->can('numify'); | |
328 | if ((defined $p) && (int($p) != $p)) | |
329 | { | |
330 | require Carp; Carp::croak ('Argument to precision must be an integer'); | |
331 | } | |
ee15d750 JH |
332 | if (ref($x)) |
333 | { | |
334 | # $object->precision() or fallback to global | |
ef9466ea T |
335 | $x->bfround($p) if $p; # not for undef, 0 |
336 | $x->{_p} = $p; # set/overwrite, even if not rounded | |
337 | delete $x->{_a}; # clear A | |
990fb837 | 338 | $p = ${"${class}::precision"} unless defined $p; # proper return value |
ee15d750 JH |
339 | } |
340 | else | |
341 | { | |
ef9466ea T |
342 | ${"${class}::precision"} = $p; # set global P |
343 | ${"${class}::accuracy"} = undef; # clear global A | |
ee15d750 | 344 | } |
ef9466ea | 345 | return $p; # shortcut |
58cde26e | 346 | } |
ee15d750 | 347 | |
f9a08e12 JH |
348 | my $r; |
349 | # $object->precision() or fallback to global | |
350 | $r = $x->{_p} if ref($x); | |
351 | # but don't return global undef, when $x's precision is 0! | |
352 | $r = ${"${class}::precision"} if !defined $r; | |
353 | $r; | |
990fb837 | 354 | } |
58cde26e | 355 | |
b3abae2a JH |
356 | sub config |
357 | { | |
990fb837 | 358 | # return (or set) configuration data as hash ref |
b3abae2a JH |
359 | my $class = shift || 'Math::BigInt'; |
360 | ||
361 | no strict 'refs'; | |
990fb837 RGS |
362 | if (@_ > 0) |
363 | { | |
364 | # try to set given options as arguments from hash | |
365 | ||
366 | my $args = $_[0]; | |
367 | if (ref($args) ne 'HASH') | |
368 | { | |
369 | $args = { @_ }; | |
370 | } | |
371 | # these values can be "set" | |
372 | my $set_args = {}; | |
373 | foreach my $key ( | |
374 | qw/trap_inf trap_nan | |
375 | upgrade downgrade precision accuracy round_mode div_scale/ | |
376 | ) | |
377 | { | |
378 | $set_args->{$key} = $args->{$key} if exists $args->{$key}; | |
379 | delete $args->{$key}; | |
380 | } | |
381 | if (keys %$args > 0) | |
382 | { | |
383 | require Carp; | |
384 | Carp::croak ("Illegal key(s) '", | |
385 | join("','",keys %$args),"' passed to $class\->config()"); | |
386 | } | |
387 | foreach my $key (keys %$set_args) | |
388 | { | |
389 | if ($key =~ /^trap_(inf|nan)\z/) | |
390 | { | |
391 | ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0); | |
392 | next; | |
393 | } | |
394 | # use a call instead of just setting the $variable to check argument | |
395 | $class->$key($set_args->{$key}); | |
396 | } | |
397 | } | |
398 | ||
399 | # now return actual configuration | |
400 | ||
b3abae2a | 401 | my $cfg = { |
990fb837 RGS |
402 | lib => $CALC, |
403 | lib_version => ${"${CALC}::VERSION"}, | |
b3abae2a | 404 | class => $class, |
990fb837 RGS |
405 | trap_nan => ${"${class}::_trap_nan"}, |
406 | trap_inf => ${"${class}::_trap_inf"}, | |
407 | version => ${"${class}::VERSION"}, | |
b3abae2a | 408 | }; |
990fb837 RGS |
409 | foreach my $key (qw/ |
410 | upgrade downgrade precision accuracy round_mode div_scale | |
411 | /) | |
b3abae2a | 412 | { |
990fb837 | 413 | $cfg->{$key} = ${"${class}::$key"}; |
b3abae2a JH |
414 | }; |
415 | $cfg; | |
416 | } | |
417 | ||
58cde26e JH |
418 | sub _scale_a |
419 | { | |
420 | # select accuracy parameter based on precedence, | |
421 | # used by bround() and bfround(), may return undef for scale (means no op) | |
422 | my ($x,$s,$m,$scale,$mode) = @_; | |
423 | $scale = $x->{_a} if !defined $scale; | |
424 | $scale = $s if (!defined $scale); | |
425 | $mode = $m if !defined $mode; | |
426 | return ($scale,$mode); | |
427 | } | |
428 | ||
429 | sub _scale_p | |
430 | { | |
431 | # select precision parameter based on precedence, | |
432 | # used by bround() and bfround(), may return undef for scale (means no op) | |
433 | my ($x,$s,$m,$scale,$mode) = @_; | |
434 | $scale = $x->{_p} if !defined $scale; | |
435 | $scale = $s if (!defined $scale); | |
436 | $mode = $m if !defined $mode; | |
437 | return ($scale,$mode); | |
438 | } | |
439 | ||
440 | ############################################################################## | |
441 | # constructors | |
442 | ||
443 | sub copy | |
444 | { | |
445 | my ($c,$x); | |
446 | if (@_ > 1) | |
447 | { | |
448 | # if two arguments, the first one is the class to "swallow" subclasses | |
449 | ($c,$x) = @_; | |
450 | } | |
451 | else | |
452 | { | |
453 | $x = shift; | |
454 | $c = ref($x); | |
455 | } | |
456 | return unless ref($x); # only for objects | |
457 | ||
458 | my $self = {}; bless $self,$c; | |
9b924220 RGS |
459 | |
460 | $self->{sign} = $x->{sign}; | |
461 | $self->{value} = $CALC->_copy($x->{value}); | |
462 | $self->{_a} = $x->{_a} if defined $x->{_a}; | |
463 | $self->{_p} = $x->{_p} if defined $x->{_p}; | |
58cde26e JH |
464 | $self; |
465 | } | |
466 | ||
467 | sub new | |
468 | { | |
b22b3e31 | 469 | # create a new BigInt object from a string or another BigInt object. |
0716bf9b | 470 | # see hash keys documented at top |
58cde26e JH |
471 | |
472 | # the argument could be an object, so avoid ||, && etc on it, this would | |
b22b3e31 PN |
473 | # cause costly overloaded code to be called. The only allowed ops are |
474 | # ref() and defined. | |
58cde26e | 475 | |
61f5c3f5 | 476 | my ($class,$wanted,$a,$p,$r) = @_; |
58cde26e | 477 | |
61f5c3f5 T |
478 | # avoid numify-calls by not using || on $wanted! |
479 | return $class->bzero($a,$p) if !defined $wanted; # default to 0 | |
9393ace2 JH |
480 | return $class->copy($wanted,$a,$p,$r) |
481 | if ref($wanted) && $wanted->isa($class); # MBI or subclass | |
58cde26e | 482 | |
61f5c3f5 T |
483 | $class->import() if $IMPORT == 0; # make require work |
484 | ||
9393ace2 JH |
485 | my $self = bless {}, $class; |
486 | ||
487 | # shortcut for "normal" numbers | |
739c8b3a | 488 | if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/)) |
9393ace2 JH |
489 | { |
490 | $self->{sign} = $1 || '+'; | |
9b924220 | 491 | |
9393ace2 JH |
492 | if ($wanted =~ /^[+-]/) |
493 | { | |
56d9de68 | 494 | # remove sign without touching wanted to make it work with constants |
9b924220 RGS |
495 | my $t = $wanted; $t =~ s/^[+-]//; |
496 | $self->{value} = $CALC->_new($t); | |
497 | } | |
498 | else | |
499 | { | |
500 | $self->{value} = $CALC->_new($wanted); | |
9393ace2 | 501 | } |
9393ace2 JH |
502 | no strict 'refs'; |
503 | if ( (defined $a) || (defined $p) | |
504 | || (defined ${"${class}::precision"}) | |
505 | || (defined ${"${class}::accuracy"}) | |
506 | ) | |
507 | { | |
508 | $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p); | |
509 | } | |
510 | return $self; | |
511 | } | |
512 | ||
58cde26e | 513 | # handle '+inf', '-inf' first |
ee15d750 | 514 | if ($wanted =~ /^[+-]?inf$/) |
58cde26e | 515 | { |
0716bf9b | 516 | $self->{value} = $CALC->_zero(); |
ee15d750 | 517 | $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf'; |
58cde26e JH |
518 | return $self; |
519 | } | |
520 | # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign | |
9b924220 | 521 | my ($mis,$miv,$mfv,$es,$ev) = _split($wanted); |
58cde26e JH |
522 | if (!ref $mis) |
523 | { | |
990fb837 RGS |
524 | if ($_trap_nan) |
525 | { | |
526 | require Carp; Carp::croak("$wanted is not a number in $class"); | |
527 | } | |
0716bf9b | 528 | $self->{value} = $CALC->_zero(); |
58cde26e JH |
529 | $self->{sign} = $nan; |
530 | return $self; | |
531 | } | |
574bacfe JH |
532 | if (!ref $miv) |
533 | { | |
534 | # _from_hex or _from_bin | |
535 | $self->{value} = $mis->{value}; | |
536 | $self->{sign} = $mis->{sign}; | |
537 | return $self; # throw away $mis | |
538 | } | |
58cde26e JH |
539 | # make integer from mantissa by adjusting exp, then convert to bigint |
540 | $self->{sign} = $$mis; # store sign | |
0716bf9b | 541 | $self->{value} = $CALC->_zero(); # for all the NaN cases |
58cde26e JH |
542 | my $e = int("$$es$$ev"); # exponent (avoid recursion) |
543 | if ($e > 0) | |
544 | { | |
545 | my $diff = $e - CORE::length($$mfv); | |
546 | if ($diff < 0) # Not integer | |
547 | { | |
990fb837 RGS |
548 | if ($_trap_nan) |
549 | { | |
550 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
551 | } | |
58cde26e | 552 | #print "NOI 1\n"; |
b3abae2a | 553 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
554 | $self->{sign} = $nan; |
555 | } | |
556 | else # diff >= 0 | |
557 | { | |
558 | # adjust fraction and add it to value | |
990fb837 | 559 | #print "diff > 0 $$miv\n"; |
58cde26e JH |
560 | $$miv = $$miv . ($$mfv . '0' x $diff); |
561 | } | |
562 | } | |
563 | else | |
564 | { | |
565 | if ($$mfv ne '') # e <= 0 | |
566 | { | |
567 | # fraction and negative/zero E => NOI | |
990fb837 RGS |
568 | if ($_trap_nan) |
569 | { | |
570 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
571 | } | |
58cde26e | 572 | #print "NOI 2 \$\$mfv '$$mfv'\n"; |
b3abae2a | 573 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
574 | $self->{sign} = $nan; |
575 | } | |
576 | elsif ($e < 0) | |
577 | { | |
578 | # xE-y, and empty mfv | |
579 | #print "xE-y\n"; | |
580 | $e = abs($e); | |
581 | if ($$miv !~ s/0{$e}$//) # can strip so many zero's? | |
582 | { | |
990fb837 RGS |
583 | if ($_trap_nan) |
584 | { | |
585 | require Carp; Carp::croak("$wanted not an integer in $class"); | |
586 | } | |
58cde26e | 587 | #print "NOI 3\n"; |
b3abae2a | 588 | return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade; |
58cde26e JH |
589 | $self->{sign} = $nan; |
590 | } | |
591 | } | |
592 | } | |
593 | $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 | |
9b924220 | 594 | $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/; |
0716bf9b | 595 | # if any of the globals is set, use them to round and store them inside $self |
61f5c3f5 T |
596 | # do not round for new($x,undef,undef) since that is used by MBF to signal |
597 | # no rounding | |
598 | $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p; | |
9393ace2 | 599 | $self; |
58cde26e JH |
600 | } |
601 | ||
58cde26e JH |
602 | sub bnan |
603 | { | |
604 | # create a bigint 'NaN', if given a BigInt, set it to 'NaN' | |
b4f14daa | 605 | my $self = shift; |
58cde26e JH |
606 | $self = $class if !defined $self; |
607 | if (!ref($self)) | |
608 | { | |
609 | my $c = $self; $self = {}; bless $self, $c; | |
610 | } | |
990fb837 RGS |
611 | no strict 'refs'; |
612 | if (${"${class}::_trap_nan"}) | |
613 | { | |
614 | require Carp; | |
615 | Carp::croak ("Tried to set $self to NaN in $class\::bnan()"); | |
616 | } | |
61f5c3f5 | 617 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 618 | return if $self->modify('bnan'); |
13a12e00 JH |
619 | if ($self->can('_bnan')) |
620 | { | |
621 | # use subclass to initialize | |
622 | $self->_bnan(); | |
623 | } | |
624 | else | |
625 | { | |
626 | # otherwise do our own thing | |
627 | $self->{value} = $CALC->_zero(); | |
628 | } | |
58cde26e | 629 | $self->{sign} = $nan; |
394e6ffb | 630 | delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly |
ef9466ea | 631 | $self; |
b4f14daa | 632 | } |
58cde26e JH |
633 | |
634 | sub binf | |
635 | { | |
636 | # create a bigint '+-inf', if given a BigInt, set it to '+-inf' | |
637 | # the sign is either '+', or if given, used from there | |
638 | my $self = shift; | |
56b9c951 | 639 | my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/; |
58cde26e JH |
640 | $self = $class if !defined $self; |
641 | if (!ref($self)) | |
642 | { | |
643 | my $c = $self; $self = {}; bless $self, $c; | |
644 | } | |
990fb837 RGS |
645 | no strict 'refs'; |
646 | if (${"${class}::_trap_inf"}) | |
647 | { | |
648 | require Carp; | |
649 | Carp::croak ("Tried to set $self to +-inf in $class\::binfn()"); | |
650 | } | |
61f5c3f5 | 651 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 652 | return if $self->modify('binf'); |
13a12e00 JH |
653 | if ($self->can('_binf')) |
654 | { | |
655 | # use subclass to initialize | |
656 | $self->_binf(); | |
657 | } | |
658 | else | |
659 | { | |
660 | # otherwise do our own thing | |
661 | $self->{value} = $CALC->_zero(); | |
662 | } | |
56b9c951 JH |
663 | $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf |
664 | $self->{sign} = $sign; | |
394e6ffb | 665 | ($self->{_a},$self->{_p}) = @_; # take over requested rounding |
ef9466ea | 666 | $self; |
58cde26e JH |
667 | } |
668 | ||
669 | sub bzero | |
670 | { | |
671 | # create a bigint '+0', if given a BigInt, set it to 0 | |
672 | my $self = shift; | |
12fc2493 | 673 | $self = __PACKAGE__ if !defined $self; |
0716bf9b | 674 | |
58cde26e JH |
675 | if (!ref($self)) |
676 | { | |
677 | my $c = $self; $self = {}; bless $self, $c; | |
678 | } | |
61f5c3f5 | 679 | $self->import() if $IMPORT == 0; # make require work |
58cde26e | 680 | return if $self->modify('bzero'); |
990fb837 | 681 | |
13a12e00 JH |
682 | if ($self->can('_bzero')) |
683 | { | |
684 | # use subclass to initialize | |
685 | $self->_bzero(); | |
686 | } | |
687 | else | |
688 | { | |
689 | # otherwise do our own thing | |
690 | $self->{value} = $CALC->_zero(); | |
691 | } | |
58cde26e | 692 | $self->{sign} = '+'; |
61f5c3f5 T |
693 | if (@_ > 0) |
694 | { | |
f9a08e12 JH |
695 | if (@_ > 3) |
696 | { | |
697 | # call like: $x->bzero($a,$p,$r,$y); | |
698 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
699 | } | |
700 | else | |
701 | { | |
702 | $self->{_a} = $_[0] | |
703 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
704 | $self->{_p} = $_[1] | |
705 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
706 | } | |
61f5c3f5 | 707 | } |
f9a08e12 | 708 | $self; |
58cde26e JH |
709 | } |
710 | ||
574bacfe JH |
711 | sub bone |
712 | { | |
713 | # create a bigint '+1' (or -1 if given sign '-'), | |
714 | # if given a BigInt, set it to +1 or -1, respecively | |
715 | my $self = shift; | |
716 | my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-'; | |
717 | $self = $class if !defined $self; | |
990fb837 | 718 | |
574bacfe JH |
719 | if (!ref($self)) |
720 | { | |
721 | my $c = $self; $self = {}; bless $self, $c; | |
722 | } | |
61f5c3f5 | 723 | $self->import() if $IMPORT == 0; # make require work |
574bacfe | 724 | return if $self->modify('bone'); |
13a12e00 JH |
725 | |
726 | if ($self->can('_bone')) | |
727 | { | |
728 | # use subclass to initialize | |
729 | $self->_bone(); | |
730 | } | |
731 | else | |
732 | { | |
733 | # otherwise do our own thing | |
734 | $self->{value} = $CALC->_one(); | |
735 | } | |
574bacfe | 736 | $self->{sign} = $sign; |
61f5c3f5 T |
737 | if (@_ > 0) |
738 | { | |
f9a08e12 JH |
739 | if (@_ > 3) |
740 | { | |
741 | # call like: $x->bone($sign,$a,$p,$r,$y); | |
742 | ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_); | |
743 | } | |
744 | else | |
745 | { | |
091c87b1 | 746 | # call like: $x->bone($sign,$a,$p,$r); |
f9a08e12 JH |
747 | $self->{_a} = $_[0] |
748 | if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); | |
749 | $self->{_p} = $_[1] | |
750 | if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); | |
751 | } | |
61f5c3f5 | 752 | } |
f9a08e12 | 753 | $self; |
574bacfe JH |
754 | } |
755 | ||
58cde26e JH |
756 | ############################################################################## |
757 | # string conversation | |
758 | ||
759 | sub bsstr | |
760 | { | |
761 | # (ref to BFLOAT or num_str ) return num_str | |
762 | # Convert number from internal format to scientific string format. | |
763 | # internal format is always normalized (no leading zeros, "-0E0" => "+0E0") | |
12fc2493 | 764 | my $x = shift; my $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
dccbb853 | 765 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 766 | |
574bacfe JH |
767 | if ($x->{sign} !~ /^[+-]$/) |
768 | { | |
769 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
770 | return 'inf'; # +inf | |
771 | } | |
58cde26e | 772 | my ($m,$e) = $x->parts(); |
b282a552 T |
773 | #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt |
774 | # 'e+' because E can only be positive in BigInt | |
9b924220 | 775 | $m->bstr() . 'e+' . $CALC->_str($e->{value}); |
58cde26e JH |
776 | } |
777 | ||
778 | sub bstr | |
779 | { | |
0716bf9b | 780 | # make a string from bigint object |
12fc2493 | 781 | my $x = shift; my $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); |
ee15d750 | 782 | # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
56b9c951 | 783 | |
574bacfe JH |
784 | if ($x->{sign} !~ /^[+-]$/) |
785 | { | |
786 | return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN | |
787 | return 'inf'; # +inf | |
788 | } | |
0716bf9b | 789 | my $es = ''; $es = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 790 | $es.$CALC->_str($x->{value}); |
58cde26e JH |
791 | } |
792 | ||
793 | sub numify | |
794 | { | |
394e6ffb | 795 | # Make a "normal" scalar from a BigInt object |
58cde26e | 796 | my $x = shift; $x = $class->new($x) unless ref $x; |
56d9de68 T |
797 | |
798 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; | |
0716bf9b JH |
799 | my $num = $CALC->_num($x->{value}); |
800 | return -$num if $x->{sign} eq '-'; | |
9393ace2 | 801 | $num; |
58cde26e JH |
802 | } |
803 | ||
804 | ############################################################################## | |
805 | # public stuff (usually prefixed with "b") | |
806 | ||
807 | sub sign | |
808 | { | |
9393ace2 | 809 | # return the sign of the number: +/-/-inf/+inf/NaN |
b282a552 | 810 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 811 | |
9393ace2 | 812 | $x->{sign}; |
58cde26e JH |
813 | } |
814 | ||
ee15d750 | 815 | sub _find_round_parameters |
58cde26e JH |
816 | { |
817 | # After any operation or when calling round(), the result is rounded by | |
818 | # regarding the A & P from arguments, local parameters, or globals. | |
61f5c3f5 | 819 | |
990fb837 RGS |
820 | # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!! |
821 | ||
61f5c3f5 T |
822 | # This procedure finds the round parameters, but it is for speed reasons |
823 | # duplicated in round. Otherwise, it is tested by the testsuite and used | |
824 | # by fdiv(). | |
990fb837 RGS |
825 | |
826 | # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P | |
827 | # were requested/defined (locally or globally or both) | |
61f5c3f5 | 828 | |
394e6ffb JH |
829 | my ($self,$a,$p,$r,@args) = @_; |
830 | # $a accuracy, if given by caller | |
831 | # $p precision, if given by caller | |
832 | # $r round_mode, if given by caller | |
833 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
58cde26e | 834 | |
17baacb7 | 835 | # leave bigfloat parts alone |
990fb837 | 836 | return ($self) if exists $self->{_f} && ($self->{_f} & MB_NEVER_ROUND) != 0; |
17baacb7 | 837 | |
394e6ffb | 838 | my $c = ref($self); # find out class of argument(s) |
574bacfe | 839 | no strict 'refs'; |
574bacfe | 840 | |
58cde26e | 841 | # now pick $a or $p, but only if we have got "arguments" |
61f5c3f5 | 842 | if (!defined $a) |
58cde26e | 843 | { |
61f5c3f5 | 844 | foreach ($self,@args) |
58cde26e JH |
845 | { |
846 | # take the defined one, or if both defined, the one that is smaller | |
847 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
848 | } | |
61f5c3f5 T |
849 | } |
850 | if (!defined $p) | |
ee15d750 | 851 | { |
61f5c3f5 T |
852 | # even if $a is defined, take $p, to signal error for both defined |
853 | foreach ($self,@args) | |
854 | { | |
855 | # take the defined one, or if both defined, the one that is bigger | |
856 | # -2 > -3, and 3 > 2 | |
857 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
858 | } | |
ee15d750 | 859 | } |
61f5c3f5 T |
860 | # if still none defined, use globals (#2) |
861 | $a = ${"$c\::accuracy"} unless defined $a; | |
862 | $p = ${"$c\::precision"} unless defined $p; | |
990fb837 RGS |
863 | |
864 | # A == 0 is useless, so undef it to signal no rounding | |
865 | $a = undef if defined $a && $a == 0; | |
61f5c3f5 T |
866 | |
867 | # no rounding today? | |
868 | return ($self) unless defined $a || defined $p; # early out | |
869 | ||
870 | # set A and set P is an fatal error | |
990fb837 | 871 | return ($self->bnan()) if defined $a && defined $p; # error |
61f5c3f5 T |
872 | |
873 | $r = ${"$c\::round_mode"} unless defined $r; | |
990fb837 RGS |
874 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/) |
875 | { | |
876 | require Carp; Carp::croak ("Unknown round mode '$r'"); | |
877 | } | |
878 | ||
879 | ($self,$a,$p,$r); | |
ee15d750 JH |
880 | } |
881 | ||
882 | sub round | |
883 | { | |
61f5c3f5 | 884 | # Round $self according to given parameters, or given second argument's |
ee15d750 | 885 | # parameters or global defaults |
ee15d750 | 886 | |
61f5c3f5 T |
887 | # for speed reasons, _find_round_parameters is embeded here: |
888 | ||
889 | my ($self,$a,$p,$r,@args) = @_; | |
890 | # $a accuracy, if given by caller | |
891 | # $p precision, if given by caller | |
892 | # $r round_mode, if given by caller | |
893 | # @args all 'other' arguments (0 for unary, 1 for binary ops) | |
894 | ||
12fc2493 AMS |
895 | # leave bigfloat parts alone (that is only used in BigRat for now and can be |
896 | # removed once we rewrote BigRat)) | |
990fb837 | 897 | return ($self) if exists $self->{_f} && ($self->{_f} & MB_NEVER_ROUND) != 0; |
61f5c3f5 T |
898 | |
899 | my $c = ref($self); # find out class of argument(s) | |
900 | no strict 'refs'; | |
901 | ||
902 | # now pick $a or $p, but only if we have got "arguments" | |
903 | if (!defined $a) | |
58cde26e | 904 | { |
61f5c3f5 T |
905 | foreach ($self,@args) |
906 | { | |
907 | # take the defined one, or if both defined, the one that is smaller | |
908 | $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); | |
909 | } | |
58cde26e | 910 | } |
61f5c3f5 T |
911 | if (!defined $p) |
912 | { | |
913 | # even if $a is defined, take $p, to signal error for both defined | |
914 | foreach ($self,@args) | |
915 | { | |
916 | # take the defined one, or if both defined, the one that is bigger | |
917 | # -2 > -3, and 3 > 2 | |
918 | $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); | |
919 | } | |
920 | } | |
921 | # if still none defined, use globals (#2) | |
922 | $a = ${"$c\::accuracy"} unless defined $a; | |
923 | $p = ${"$c\::precision"} unless defined $p; | |
924 | ||
990fb837 RGS |
925 | # A == 0 is useless, so undef it to signal no rounding |
926 | $a = undef if defined $a && $a == 0; | |
927 | ||
61f5c3f5 T |
928 | # no rounding today? |
929 | return $self unless defined $a || defined $p; # early out | |
930 | ||
931 | # set A and set P is an fatal error | |
932 | return $self->bnan() if defined $a && defined $p; | |
933 | ||
934 | $r = ${"$c\::round_mode"} unless defined $r; | |
990fb837 RGS |
935 | if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/) |
936 | { | |
b282a552 | 937 | require Carp; Carp::croak ("Unknown round mode '$r'"); |
990fb837 | 938 | } |
61f5c3f5 T |
939 | |
940 | # now round, by calling either fround or ffround: | |
941 | if (defined $a) | |
942 | { | |
943 | $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a; | |
944 | } | |
945 | else # both can't be undefined due to early out | |
58cde26e | 946 | { |
61f5c3f5 | 947 | $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p; |
58cde26e | 948 | } |
12fc2493 AMS |
949 | # bround() or bfround() already callled bnorm() if necc. |
950 | $self; | |
58cde26e JH |
951 | } |
952 | ||
17baacb7 | 953 | sub bnorm |
58cde26e | 954 | { |
027dc388 | 955 | # (numstr or BINT) return BINT |
58cde26e | 956 | # Normalize number -- no-op here |
b282a552 | 957 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
b3abae2a | 958 | $x; |
58cde26e JH |
959 | } |
960 | ||
961 | sub babs | |
962 | { | |
963 | # (BINT or num_str) return BINT | |
964 | # make number absolute, or return absolute BINT from string | |
ee15d750 JH |
965 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
966 | ||
58cde26e JH |
967 | return $x if $x->modify('babs'); |
968 | # post-normalized abs for internal use (does nothing for NaN) | |
969 | $x->{sign} =~ s/^-/+/; | |
970 | $x; | |
971 | } | |
972 | ||
973 | sub bneg | |
974 | { | |
975 | # (BINT or num_str) return BINT | |
976 | # negate number or make a negated number from string | |
ee15d750 JH |
977 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
978 | ||
58cde26e | 979 | return $x if $x->modify('bneg'); |
b3abae2a | 980 | |
58cde26e | 981 | # for +0 dont negate (to have always normalized) |
b3abae2a | 982 | $x->{sign} =~ tr/+-/-+/ if !$x->is_zero(); # does nothing for NaN |
58cde26e JH |
983 | $x; |
984 | } | |
985 | ||
986 | sub bcmp | |
987 | { | |
988 | # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) | |
989 | # (BINT or num_str, BINT or num_str) return cond_code | |
f9a08e12 JH |
990 | |
991 | # set up parameters | |
992 | my ($self,$x,$y) = (ref($_[0]),@_); | |
993 | ||
994 | # objectify is costly, so avoid it | |
995 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
996 | { | |
997 | ($self,$x,$y) = objectify(2,@_); | |
998 | } | |
0716bf9b | 999 | |
56d9de68 T |
1000 | return $upgrade->bcmp($x,$y) if defined $upgrade && |
1001 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1002 | ||
0716bf9b JH |
1003 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1004 | { | |
1005 | # handle +-inf and NaN | |
1006 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
574bacfe | 1007 | return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; |
0716bf9b JH |
1008 | return +1 if $x->{sign} eq '+inf'; |
1009 | return -1 if $x->{sign} eq '-inf'; | |
1010 | return -1 if $y->{sign} eq '+inf'; | |
b3abae2a | 1011 | return +1; |
0716bf9b | 1012 | } |
574bacfe JH |
1013 | # check sign for speed first |
1014 | return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y | |
1015 | return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 | |
1016 | ||
f9a08e12 JH |
1017 | # have same sign, so compare absolute values. Don't make tests for zero here |
1018 | # because it's actually slower than testin in Calc (especially w/ Pari et al) | |
1019 | ||
dccbb853 JH |
1020 | # post-normalized compare for internal use (honors signs) |
1021 | if ($x->{sign} eq '+') | |
1022 | { | |
56b9c951 | 1023 | # $x and $y both > 0 |
dccbb853 JH |
1024 | return $CALC->_acmp($x->{value},$y->{value}); |
1025 | } | |
1026 | ||
56b9c951 | 1027 | # $x && $y both < 0 |
b282a552 | 1028 | $CALC->_acmp($y->{value},$x->{value}); # swaped acmp (lib returns 0,1,-1) |
58cde26e JH |
1029 | } |
1030 | ||
1031 | sub bacmp | |
1032 | { | |
1033 | # Compares 2 values, ignoring their signs. | |
1034 | # Returns one of undef, <0, =0, >0. (suitable for sort) | |
1035 | # (BINT, BINT) return cond_code | |
574bacfe | 1036 | |
f9a08e12 JH |
1037 | # set up parameters |
1038 | my ($self,$x,$y) = (ref($_[0]),@_); | |
1039 | # objectify is costly, so avoid it | |
1040 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1041 | { | |
1042 | ($self,$x,$y) = objectify(2,@_); | |
1043 | } | |
1044 | ||
56d9de68 T |
1045 | return $upgrade->bacmp($x,$y) if defined $upgrade && |
1046 | ((!$x->isa($self)) || (!$y->isa($self))); | |
1047 | ||
574bacfe JH |
1048 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) |
1049 | { | |
1050 | # handle +-inf and NaN | |
1051 | return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
1052 | return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; | |
ef9466ea T |
1053 | return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; |
1054 | return -1; | |
574bacfe | 1055 | } |
b3abae2a | 1056 | $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1 |
58cde26e JH |
1057 | } |
1058 | ||
1059 | sub badd | |
1060 | { | |
1061 | # add second arg (BINT or string) to first (BINT) (modifies first) | |
1062 | # return result as BINT | |
f9a08e12 JH |
1063 | |
1064 | # set up parameters | |
1065 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1066 | # objectify is costly, so avoid it | |
1067 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1068 | { | |
1069 | ($self,$x,$y,@r) = objectify(2,@_); | |
1070 | } | |
58cde26e JH |
1071 | |
1072 | return $x if $x->modify('badd'); | |
091c87b1 | 1073 | return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade && |
8f675a64 | 1074 | ((!$x->isa($self)) || (!$y->isa($self))); |
58cde26e | 1075 | |
61f5c3f5 | 1076 | $r[3] = $y; # no push! |
574bacfe JH |
1077 | # inf and NaN handling |
1078 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) | |
1079 | { | |
1080 | # NaN first | |
1081 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); | |
13a12e00 JH |
1082 | # inf handling |
1083 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
574bacfe | 1084 | { |
b3abae2a JH |
1085 | # +inf++inf or -inf+-inf => same, rest is NaN |
1086 | return $x if $x->{sign} eq $y->{sign}; | |
1087 | return $x->bnan(); | |
574bacfe JH |
1088 | } |
1089 | # +-inf + something => +inf | |
1090 | # something +-inf => +-inf | |
1091 | $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; | |
1092 | return $x; | |
1093 | } | |
1094 | ||
b282a552 | 1095 | my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs |
58cde26e JH |
1096 | |
1097 | if ($sx eq $sy) | |
1098 | { | |
574bacfe | 1099 | $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add |
58cde26e JH |
1100 | } |
1101 | else | |
1102 | { | |
574bacfe | 1103 | my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare |
58cde26e JH |
1104 | if ($a > 0) |
1105 | { | |
574bacfe | 1106 | $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap |
58cde26e JH |
1107 | $x->{sign} = $sy; |
1108 | } | |
1109 | elsif ($a == 0) | |
1110 | { | |
1111 | # speedup, if equal, set result to 0 | |
0716bf9b | 1112 | $x->{value} = $CALC->_zero(); |
58cde26e JH |
1113 | $x->{sign} = '+'; |
1114 | } | |
1115 | else # a < 0 | |
1116 | { | |
574bacfe | 1117 | $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub |
a0d0e21e | 1118 | } |
a0d0e21e | 1119 | } |
f9a08e12 JH |
1120 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
1121 | $x; | |
58cde26e JH |
1122 | } |
1123 | ||
1124 | sub bsub | |
1125 | { | |
091c87b1 | 1126 | # (BINT or num_str, BINT or num_str) return BINT |
58cde26e | 1127 | # subtract second arg from first, modify first |
f9a08e12 JH |
1128 | |
1129 | # set up parameters | |
1130 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1131 | # objectify is costly, so avoid it | |
1132 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1133 | { | |
1134 | ($self,$x,$y,@r) = objectify(2,@_); | |
1135 | } | |
58cde26e | 1136 | |
58cde26e | 1137 | return $x if $x->modify('bsub'); |
8f675a64 | 1138 | |
9b924220 RGS |
1139 | return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade && |
1140 | ((!$x->isa($self)) || (!$y->isa($self))); | |
b3abae2a JH |
1141 | |
1142 | if ($y->is_zero()) | |
1143 | { | |
f9a08e12 JH |
1144 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
1145 | return $x; | |
e745a66c | 1146 | } |
b3abae2a | 1147 | |
ae161977 RGS |
1148 | require Scalar::Util; |
1149 | if (Scalar::Util::refaddr($x) == Scalar::Util::refaddr($y)) | |
03874afe T |
1150 | { |
1151 | # if we get the same variable twice, the result must be zero (the code | |
1152 | # below fails in that case) | |
1153 | return $x->bzero(@r) if $x->{sign} =~ /^[+-]$/; | |
1154 | return $x->bnan(); # NaN, -inf, +inf | |
1155 | } | |
b3abae2a JH |
1156 | $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN |
1157 | $x->badd($y,@r); # badd does not leave internal zeros | |
1158 | $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN) | |
61f5c3f5 | 1159 | $x; # already rounded by badd() or no round necc. |
58cde26e JH |
1160 | } |
1161 | ||
1162 | sub binc | |
1163 | { | |
1164 | # increment arg by one | |
ee15d750 | 1165 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1166 | return $x if $x->modify('binc'); |
e745a66c JH |
1167 | |
1168 | if ($x->{sign} eq '+') | |
1169 | { | |
1170 | $x->{value} = $CALC->_inc($x->{value}); | |
f9a08e12 JH |
1171 | $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
1172 | return $x; | |
e745a66c JH |
1173 | } |
1174 | elsif ($x->{sign} eq '-') | |
1175 | { | |
1176 | $x->{value} = $CALC->_dec($x->{value}); | |
1177 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 | |
f9a08e12 JH |
1178 | $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
1179 | return $x; | |
e745a66c JH |
1180 | } |
1181 | # inf, nan handling etc | |
091c87b1 | 1182 | $x->badd($self->bone(),$a,$p,$r); # badd does round |
58cde26e JH |
1183 | } |
1184 | ||
1185 | sub bdec | |
1186 | { | |
1187 | # decrement arg by one | |
b282a552 | 1188 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1189 | return $x if $x->modify('bdec'); |
e745a66c | 1190 | |
b282a552 | 1191 | if ($x->{sign} eq '-') |
e745a66c | 1192 | { |
b282a552 | 1193 | # < 0 |
e745a66c | 1194 | $x->{value} = $CALC->_inc($x->{value}); |
b282a552 T |
1195 | } |
1196 | else | |
e745a66c | 1197 | { |
b282a552 T |
1198 | return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf/NaN |
1199 | # >= 0 | |
1200 | if ($CALC->_is_zero($x->{value})) | |
1201 | { | |
1202 | # == 0 | |
1203 | $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1 | |
1204 | } | |
1205 | else | |
1206 | { | |
1207 | # > 0 | |
1208 | $x->{value} = $CALC->_dec($x->{value}); | |
1209 | } | |
e745a66c | 1210 | } |
b282a552 T |
1211 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
1212 | $x; | |
1213 | } | |
58cde26e | 1214 | |
61f5c3f5 T |
1215 | sub blog |
1216 | { | |
091c87b1 T |
1217 | # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base |
1218 | # $base of $x) | |
1219 | ||
1220 | # set up parameters | |
1221 | my ($self,$x,$base,@r) = (ref($_[0]),@_); | |
1222 | # objectify is costly, so avoid it | |
1223 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1224 | { | |
9b924220 | 1225 | ($self,$x,$base,@r) = objectify(1,$class,@_); |
091c87b1 | 1226 | } |
9b924220 | 1227 | |
ef9466ea T |
1228 | return $x if $x->modify('blog'); |
1229 | ||
091c87b1 T |
1230 | # inf, -inf, NaN, <0 => NaN |
1231 | return $x->bnan() | |
9b924220 | 1232 | if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+'); |
091c87b1 | 1233 | |
9b924220 RGS |
1234 | return $upgrade->blog($upgrade->new($x),$base,@r) if |
1235 | defined $upgrade; | |
091c87b1 | 1236 | |
9b924220 RGS |
1237 | my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value}); |
1238 | return $x->bnan() unless defined $rc; # not possible to take log? | |
1239 | $x->{value} = $rc; | |
1240 | $x->round(@r); | |
61f5c3f5 | 1241 | } |
091c87b1 | 1242 | |
58cde26e JH |
1243 | sub blcm |
1244 | { | |
1245 | # (BINT or num_str, BINT or num_str) return BINT | |
1246 | # does not modify arguments, but returns new object | |
1247 | # Lowest Common Multiplicator | |
58cde26e | 1248 | |
0716bf9b JH |
1249 | my $y = shift; my ($x); |
1250 | if (ref($y)) | |
1251 | { | |
1252 | $x = $y->copy(); | |
1253 | } | |
1254 | else | |
1255 | { | |
12fc2493 | 1256 | $x = $class->new($y); |
0716bf9b | 1257 | } |
9b924220 RGS |
1258 | my $self = ref($x); |
1259 | while (@_) | |
1260 | { | |
1261 | my $y = shift; $y = $self->new($y) if !ref ($y); | |
1262 | $x = __lcm($x,$y); | |
1263 | } | |
58cde26e JH |
1264 | $x; |
1265 | } | |
1266 | ||
1267 | sub bgcd | |
1268 | { | |
1269 | # (BINT or num_str, BINT or num_str) return BINT | |
1270 | # does not modify arguments, but returns new object | |
1271 | # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff) | |
0716bf9b | 1272 | |
dccbb853 | 1273 | my $y = shift; |
12fc2493 | 1274 | $y = $class->new($y) if !ref($y); |
dccbb853 | 1275 | my $self = ref($y); |
9b924220 RGS |
1276 | my $x = $y->copy()->babs(); # keep arguments |
1277 | return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN? | |
1278 | ||
1279 | while (@_) | |
0716bf9b | 1280 | { |
9b924220 RGS |
1281 | $y = shift; $y = $self->new($y) if !ref($y); |
1282 | next if $y->is_zero(); | |
1283 | return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? | |
1284 | $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one(); | |
0716bf9b | 1285 | } |
9b924220 | 1286 | $x; |
58cde26e JH |
1287 | } |
1288 | ||
58cde26e JH |
1289 | sub bnot |
1290 | { | |
1291 | # (num_str or BINT) return BINT | |
1292 | # represent ~x as twos-complement number | |
ee15d750 JH |
1293 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
1294 | my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
1295 | ||
58cde26e | 1296 | return $x if $x->modify('bnot'); |
091c87b1 | 1297 | $x->binc()->bneg(); # binc already does round |
58cde26e JH |
1298 | } |
1299 | ||
091c87b1 | 1300 | ############################################################################## |
b3abae2a | 1301 | # is_foo test routines |
091c87b1 | 1302 | # we don't need $self, so undef instead of ref($_[0]) make it slightly faster |
b3abae2a | 1303 | |
58cde26e JH |
1304 | sub is_zero |
1305 | { | |
1306 | # return true if arg (BINT or num_str) is zero (array '+', '0') | |
ee15d750 | 1307 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1308 | |
574bacfe | 1309 | return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't |
17baacb7 | 1310 | $CALC->_is_zero($x->{value}); |
58cde26e JH |
1311 | } |
1312 | ||
1313 | sub is_nan | |
1314 | { | |
1315 | # return true if arg (BINT or num_str) is NaN | |
091c87b1 | 1316 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
ee15d750 | 1317 | |
091c87b1 | 1318 | $x->{sign} eq $nan ? 1 : 0; |
58cde26e JH |
1319 | } |
1320 | ||
1321 | sub is_inf | |
1322 | { | |
1323 | # return true if arg (BINT or num_str) is +-inf | |
091c87b1 | 1324 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 1325 | |
091c87b1 | 1326 | if (defined $sign) |
ee15d750 | 1327 | { |
091c87b1 T |
1328 | $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf |
1329 | $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-' | |
1330 | return $x->{sign} =~ /^$sign$/ ? 1 : 0; | |
ee15d750 | 1331 | } |
091c87b1 | 1332 | $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity |
58cde26e JH |
1333 | } |
1334 | ||
1335 | sub is_one | |
1336 | { | |
091c87b1 | 1337 | # return true if arg (BINT or num_str) is +1, or -1 if sign is given |
ee15d750 JH |
1338 | my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
1339 | ||
990fb837 | 1340 | $sign = '+' if !defined $sign || $sign ne '-'; |
0716bf9b | 1341 | |
ee15d750 | 1342 | return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either |
394e6ffb | 1343 | $CALC->_is_one($x->{value}); |
58cde26e JH |
1344 | } |
1345 | ||
1346 | sub is_odd | |
1347 | { | |
1348 | # return true when arg (BINT or num_str) is odd, false for even | |
ee15d750 | 1349 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1350 | |
b22b3e31 | 1351 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1352 | $CALC->_is_odd($x->{value}); |
58cde26e JH |
1353 | } |
1354 | ||
1355 | sub is_even | |
1356 | { | |
1357 | # return true when arg (BINT or num_str) is even, false for odd | |
ee15d750 | 1358 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
0716bf9b | 1359 | |
b22b3e31 | 1360 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't |
394e6ffb | 1361 | $CALC->_is_even($x->{value}); |
0716bf9b JH |
1362 | } |
1363 | ||
1364 | sub is_positive | |
1365 | { | |
1366 | # return true when arg (BINT or num_str) is positive (>= 0) | |
ee15d750 JH |
1367 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1368 | ||
091c87b1 | 1369 | $x->{sign} =~ /^\+/ ? 1 : 0; # +inf is also positive, but NaN not |
0716bf9b JH |
1370 | } |
1371 | ||
1372 | sub is_negative | |
1373 | { | |
1374 | # return true when arg (BINT or num_str) is negative (< 0) | |
ee15d750 JH |
1375 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1376 | ||
091c87b1 | 1377 | $x->{sign} =~ /^-/ ? 1 : 0; # -inf is also negative, but NaN not |
58cde26e JH |
1378 | } |
1379 | ||
b3abae2a JH |
1380 | sub is_int |
1381 | { | |
1382 | # return true when arg (BINT or num_str) is an integer | |
091c87b1 | 1383 | # always true for BigInt, but different for BigFloats |
b3abae2a JH |
1384 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
1385 | ||
1386 | $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't | |
1387 | } | |
1388 | ||
0716bf9b JH |
1389 | ############################################################################### |
1390 | ||
58cde26e JH |
1391 | sub bmul |
1392 | { | |
1393 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 | |
1394 | # (BINT or num_str, BINT or num_str) return BINT | |
f9a08e12 JH |
1395 | |
1396 | # set up parameters | |
1397 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1398 | # objectify is costly, so avoid it | |
1399 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1400 | { | |
1401 | ($self,$x,$y,@r) = objectify(2,@_); | |
1402 | } | |
0716bf9b | 1403 | |
58cde26e | 1404 | return $x if $x->modify('bmul'); |
61f5c3f5 | 1405 | |
574bacfe | 1406 | return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); |
b3abae2a | 1407 | |
574bacfe JH |
1408 | # inf handling |
1409 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1410 | { | |
b3abae2a | 1411 | return $x->bnan() if $x->is_zero() || $y->is_zero(); |
574bacfe JH |
1412 | # result will always be +-inf: |
1413 | # +inf * +/+inf => +inf, -inf * -/-inf => +inf | |
1414 | # +inf * -/-inf => -inf, -inf * +/+inf => -inf | |
1415 | return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); | |
1416 | return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); | |
1417 | return $x->binf('-'); | |
1418 | } | |
9b924220 RGS |
1419 | |
1420 | return $upgrade->bmul($x,$upgrade->new($y),@r) | |
1421 | if defined $upgrade && !$y->isa($self); | |
9393ace2 JH |
1422 | |
1423 | $r[3] = $y; # no push here | |
58cde26e | 1424 | |
0716bf9b | 1425 | $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + |
dccbb853 | 1426 | |
b3abae2a JH |
1427 | $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math |
1428 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 | |
f9a08e12 JH |
1429 | |
1430 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; | |
1431 | $x; | |
dccbb853 JH |
1432 | } |
1433 | ||
1434 | sub _div_inf | |
1435 | { | |
1436 | # helper function that handles +-inf cases for bdiv()/bmod() to reuse code | |
1437 | my ($self,$x,$y) = @_; | |
1438 | ||
1439 | # NaN if x == NaN or y == NaN or x==y==0 | |
1440 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan() | |
1441 | if (($x->is_nan() || $y->is_nan()) || | |
1442 | ($x->is_zero() && $y->is_zero())); | |
1443 | ||
b3abae2a JH |
1444 | # +-inf / +-inf == NaN, reminder also NaN |
1445 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
dccbb853 | 1446 | { |
b3abae2a | 1447 | return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan(); |
dccbb853 JH |
1448 | } |
1449 | # x / +-inf => 0, remainder x (works even if x == 0) | |
1450 | if ($y->{sign} =~ /^[+-]inf$/) | |
1451 | { | |
f9a08e12 | 1452 | my $t = $x->copy(); # bzero clobbers up $x |
dccbb853 JH |
1453 | return wantarray ? ($x->bzero(),$t) : $x->bzero() |
1454 | } | |
1455 | ||
1456 | # 5 / 0 => +inf, -6 / 0 => -inf | |
1457 | # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf | |
1458 | # exception: -8 / 0 has remainder -8, not 8 | |
1459 | # exception: -inf / 0 has remainder -inf, not inf | |
1460 | if ($y->is_zero()) | |
1461 | { | |
1462 | # +-inf / 0 => special case for -inf | |
1463 | return wantarray ? ($x,$x->copy()) : $x if $x->is_inf(); | |
1464 | if (!$x->is_zero() && !$x->is_inf()) | |
1465 | { | |
1466 | my $t = $x->copy(); # binf clobbers up $x | |
1467 | return wantarray ? | |
1468 | ($x->binf($x->{sign}),$t) : $x->binf($x->{sign}) | |
1469 | } | |
1470 | } | |
1471 | ||
1472 | # last case: +-inf / ordinary number | |
1473 | my $sign = '+inf'; | |
1474 | $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign}; | |
1475 | $x->{sign} = $sign; | |
1476 | return wantarray ? ($x,$self->bzero()) : $x; | |
58cde26e JH |
1477 | } |
1478 | ||
1479 | sub bdiv | |
1480 | { | |
1481 | # (dividend: BINT or num_str, divisor: BINT or num_str) return | |
1482 | # (BINT,BINT) (quo,rem) or BINT (only rem) | |
f9a08e12 JH |
1483 | |
1484 | # set up parameters | |
1485 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1486 | # objectify is costly, so avoid it | |
1487 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1488 | { | |
1489 | ($self,$x,$y,@r) = objectify(2,@_); | |
1490 | } | |
58cde26e JH |
1491 | |
1492 | return $x if $x->modify('bdiv'); | |
1493 | ||
dccbb853 JH |
1494 | return $self->_div_inf($x,$y) |
1495 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()); | |
58cde26e | 1496 | |
9393ace2 JH |
1497 | return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r) |
1498 | if defined $upgrade; | |
58cde26e | 1499 | |
990fb837 RGS |
1500 | $r[3] = $y; # no push! |
1501 | ||
58cde26e | 1502 | # calc new sign and in case $y == +/- 1, return $x |
dccbb853 | 1503 | my $xsign = $x->{sign}; # keep |
58cde26e | 1504 | $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); |
58cde26e | 1505 | |
58cde26e JH |
1506 | if (wantarray) |
1507 | { | |
394e6ffb JH |
1508 | my $rem = $self->bzero(); |
1509 | ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value}); | |
1510 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
f9a08e12 JH |
1511 | $rem->{_a} = $x->{_a}; |
1512 | $rem->{_p} = $x->{_p}; | |
990fb837 | 1513 | $x->round(@r) if !exists $x->{_f} || ($x->{_f} & MB_NEVER_ROUND) == 0; |
dccbb853 JH |
1514 | if (! $CALC->_is_zero($rem->{value})) |
1515 | { | |
1516 | $rem->{sign} = $y->{sign}; | |
990fb837 | 1517 | $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-' |
dccbb853 JH |
1518 | } |
1519 | else | |
1520 | { | |
1521 | $rem->{sign} = '+'; # dont leave -0 | |
1522 | } | |
990fb837 RGS |
1523 | $rem->round(@r) if !exists $rem->{_f} || ($rem->{_f} & MB_NEVER_ROUND) == 0; |
1524 | return ($x,$rem); | |
58cde26e | 1525 | } |
394e6ffb JH |
1526 | |
1527 | $x->{value} = $CALC->_div($x->{value},$y->{value}); | |
1528 | $x->{sign} = '+' if $CALC->_is_zero($x->{value}); | |
f9a08e12 | 1529 | |
990fb837 | 1530 | $x->round(@r) if !exists $x->{_f} || ($x->{_f} & MB_NEVER_ROUND) == 0; |
f9a08e12 | 1531 | $x; |
58cde26e JH |
1532 | } |
1533 | ||
d614cd8b JH |
1534 | ############################################################################### |
1535 | # modulus functions | |
1536 | ||
dccbb853 JH |
1537 | sub bmod |
1538 | { | |
1539 | # modulus (or remainder) | |
1540 | # (BINT or num_str, BINT or num_str) return BINT | |
f9a08e12 JH |
1541 | |
1542 | # set up parameters | |
1543 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1544 | # objectify is costly, so avoid it | |
1545 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1546 | { | |
1547 | ($self,$x,$y,@r) = objectify(2,@_); | |
1548 | } | |
28df3e88 | 1549 | |
dccbb853 | 1550 | return $x if $x->modify('bmod'); |
61f5c3f5 | 1551 | $r[3] = $y; # no push! |
dccbb853 JH |
1552 | if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero()) |
1553 | { | |
1554 | my ($d,$r) = $self->_div_inf($x,$y); | |
f9a08e12 JH |
1555 | $x->{sign} = $r->{sign}; |
1556 | $x->{value} = $r->{value}; | |
1557 | return $x->round(@r); | |
dccbb853 JH |
1558 | } |
1559 | ||
9b924220 RGS |
1560 | # calc new sign and in case $y == +/- 1, return $x |
1561 | $x->{value} = $CALC->_mod($x->{value},$y->{value}); | |
1562 | if (!$CALC->_is_zero($x->{value})) | |
dccbb853 | 1563 | { |
9b924220 RGS |
1564 | my $xsign = $x->{sign}; |
1565 | $x->{sign} = $y->{sign}; | |
1566 | if ($xsign ne $y->{sign}) | |
dccbb853 | 1567 | { |
9b924220 RGS |
1568 | my $t = $CALC->_copy($x->{value}); # copy $x |
1569 | $x->{value} = $CALC->_sub($y->{value},$t,1); # $y-$x | |
dccbb853 JH |
1570 | } |
1571 | } | |
9b924220 | 1572 | else |
b3abae2a | 1573 | { |
9b924220 | 1574 | $x->{sign} = '+'; # dont leave -0 |
b3abae2a | 1575 | } |
9b924220 | 1576 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; |
b3abae2a | 1577 | $x; |
dccbb853 JH |
1578 | } |
1579 | ||
07d34614 | 1580 | sub bmodinv |
d614cd8b | 1581 | { |
56d9de68 | 1582 | # Modular inverse. given a number which is (hopefully) relatively |
d614cd8b | 1583 | # prime to the modulus, calculate its inverse using Euclid's |
56d9de68 | 1584 | # alogrithm. If the number is not relatively prime to the modulus |
d614cd8b JH |
1585 | # (i.e. their gcd is not one) then NaN is returned. |
1586 | ||
f9a08e12 JH |
1587 | # set up parameters |
1588 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
56d9de68 | 1589 | # objectify is costly, so avoid it |
f9a08e12 JH |
1590 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) |
1591 | { | |
1592 | ($self,$x,$y,@r) = objectify(2,@_); | |
56d9de68 | 1593 | } |
d614cd8b | 1594 | |
f9a08e12 | 1595 | return $x if $x->modify('bmodinv'); |
d614cd8b | 1596 | |
f9a08e12 | 1597 | return $x->bnan() |
56d9de68 T |
1598 | if ($y->{sign} ne '+' # -, NaN, +inf, -inf |
1599 | || $x->is_zero() # or num == 0 | |
1600 | || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf | |
d614cd8b | 1601 | ); |
1ddff52a | 1602 | |
f9a08e12 JH |
1603 | # put least residue into $x if $x was negative, and thus make it positive |
1604 | $x->bmod($y) if $x->{sign} eq '-'; | |
07d34614 | 1605 | |
9b924220 RGS |
1606 | my $sign; |
1607 | ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value}); | |
1608 | return $x->bnan() if !defined $x->{value}; # in case no GCD found | |
1609 | return $x if !defined $sign; # already real result | |
1610 | $x->{sign} = $sign; # flip/flop see below | |
1611 | $x->bmod($y); # calc real result | |
1612 | $x; | |
d614cd8b JH |
1613 | } |
1614 | ||
07d34614 | 1615 | sub bmodpow |
d614cd8b JH |
1616 | { |
1617 | # takes a very large number to a very large exponent in a given very | |
1618 | # large modulus, quickly, thanks to binary exponentation. supports | |
1619 | # negative exponents. | |
1620 | my ($self,$num,$exp,$mod,@r) = objectify(3,@_); | |
1621 | ||
1622 | return $num if $num->modify('bmodpow'); | |
1623 | ||
1624 | # check modulus for valid values | |
1625 | return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf | |
1626 | || $mod->is_zero()); | |
1627 | ||
1628 | # check exponent for valid values | |
1629 | if ($exp->{sign} =~ /\w/) | |
1630 | { | |
1631 | # i.e., if it's NaN, +inf, or -inf... | |
1632 | return $num->bnan(); | |
1633 | } | |
07d34614 | 1634 | |
1ddff52a | 1635 | $num->bmodinv ($mod) if ($exp->{sign} eq '-'); |
d614cd8b | 1636 | |
1ddff52a | 1637 | # check num for valid values (also NaN if there was no inverse but $exp < 0) |
07d34614 | 1638 | return $num->bnan() if $num->{sign} !~ /^[+-]$/; |
d614cd8b | 1639 | |
9b924220 RGS |
1640 | # $mod is positive, sign on $exp is ignored, result also positive |
1641 | $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value}); | |
1642 | $num; | |
d614cd8b JH |
1643 | } |
1644 | ||
1645 | ############################################################################### | |
1646 | ||
b3abae2a JH |
1647 | sub bfac |
1648 | { | |
1649 | # (BINT or num_str, BINT or num_str) return BINT | |
091c87b1 | 1650 | # compute factorial number from $x, modify $x in place |
f9a08e12 | 1651 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
b3abae2a JH |
1652 | |
1653 | return $x if $x->modify('bfac'); | |
1654 | ||
b282a552 T |
1655 | return $x if $x->{sign} eq '+inf'; # inf => inf |
1656 | return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN | |
b3abae2a | 1657 | |
9b924220 RGS |
1658 | $x->{value} = $CALC->_fac($x->{value}); |
1659 | $x->round(@r); | |
b3abae2a JH |
1660 | } |
1661 | ||
58cde26e JH |
1662 | sub bpow |
1663 | { | |
1664 | # (BINT or num_str, BINT or num_str) return BINT | |
1665 | # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 | |
1666 | # modifies first argument | |
aef458a0 | 1667 | |
f9a08e12 JH |
1668 | # set up parameters |
1669 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1670 | # objectify is costly, so avoid it | |
1671 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1672 | { | |
1673 | ($self,$x,$y,@r) = objectify(2,@_); | |
1674 | } | |
58cde26e JH |
1675 | |
1676 | return $x if $x->modify('bpow'); | |
9393ace2 | 1677 | |
2d2b2744 T |
1678 | return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; |
1679 | ||
1680 | # inf handling | |
1681 | if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) | |
1682 | { | |
1683 | if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) | |
1684 | { | |
1685 | # +-inf ** +-inf | |
1686 | return $x->bnan(); | |
1687 | } | |
1688 | # +-inf ** Y | |
1689 | if ($x->{sign} =~ /^[+-]inf/) | |
1690 | { | |
1691 | # +inf ** 0 => NaN | |
1692 | return $x->bnan() if $y->is_zero(); | |
1693 | # -inf ** -1 => 1/inf => 0 | |
1694 | return $x->bzero() if $y->is_one('-') && $x->is_negative(); | |
1695 | ||
1696 | # +inf ** Y => inf | |
1697 | return $x if $x->{sign} eq '+inf'; | |
1698 | ||
1699 | # -inf ** Y => -inf if Y is odd | |
1700 | return $x if $y->is_odd(); | |
1701 | return $x->babs(); | |
1702 | } | |
1703 | # X ** +-inf | |
1704 | ||
1705 | # 1 ** +inf => 1 | |
1706 | return $x if $x->is_one(); | |
1707 | ||
1708 | # 0 ** inf => 0 | |
1709 | return $x if $x->is_zero() && $y->{sign} =~ /^[+]/; | |
1710 | ||
1711 | # 0 ** -inf => inf | |
1712 | return $x->binf() if $x->is_zero(); | |
1713 | ||
1714 | # -1 ** -inf => NaN | |
1715 | return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/; | |
1716 | ||
1717 | # -X ** -inf => 0 | |
1718 | return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/; | |
1719 | ||
1720 | # -1 ** inf => NaN | |
1721 | return $x->bnan() if $x->{sign} eq '-'; | |
1722 | ||
1723 | # X ** inf => inf | |
1724 | return $x->binf() if $y->{sign} =~ /^[+]/; | |
1725 | # X ** -inf => 0 | |
1726 | return $x->bzero(); | |
1727 | } | |
1728 | ||
9393ace2 | 1729 | return $upgrade->bpow($upgrade->new($x),$y,@r) |
8f675a64 | 1730 | if defined $upgrade && !$y->isa($self); |
9393ace2 | 1731 | |
61f5c3f5 | 1732 | $r[3] = $y; # no push! |
b282a552 T |
1733 | |
1734 | # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu | |
1735 | ||
9b924220 RGS |
1736 | my $new_sign = '+'; |
1737 | $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+'); | |
1738 | ||
1739 | # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf | |
1740 | return $x->binf() | |
1741 | if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value}); | |
574bacfe JH |
1742 | # 1 ** -y => 1 / (1 ** |y|) |
1743 | # so do test for negative $y after above's clause | |
9b924220 | 1744 | return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value}); |
027dc388 | 1745 | |
9b924220 RGS |
1746 | $x->{value} = $CALC->_pow($x->{value},$y->{value}); |
1747 | $x->{sign} = $new_sign; | |
1748 | $x->{sign} = '+' if $CALC->_is_zero($y->{value}); | |
1749 | $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0; | |
1750 | $x; | |
58cde26e JH |
1751 | } |
1752 | ||
1753 | sub blsft | |
1754 | { | |
1755 | # (BINT or num_str, BINT or num_str) return BINT | |
1756 | # compute x << y, base n, y >= 0 | |
f9a08e12 JH |
1757 | |
1758 | # set up parameters | |
1759 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1760 | # objectify is costly, so avoid it | |
1761 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1762 | { | |
1763 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1764 | } | |
1765 | ||
58cde26e JH |
1766 | return $x if $x->modify('blsft'); |
1767 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
f9a08e12 | 1768 | return $x->round(@r) if $y->is_zero(); |
58cde26e | 1769 | |
574bacfe JH |
1770 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; |
1771 | ||
9b924220 RGS |
1772 | $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n); |
1773 | $x->round(@r); | |
58cde26e JH |
1774 | } |
1775 | ||
1776 | sub brsft | |
1777 | { | |
1778 | # (BINT or num_str, BINT or num_str) return BINT | |
1779 | # compute x >> y, base n, y >= 0 | |
f9a08e12 JH |
1780 | |
1781 | # set up parameters | |
1782 | my ($self,$x,$y,$n,@r) = (ref($_[0]),@_); | |
1783 | # objectify is costly, so avoid it | |
1784 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1785 | { | |
1786 | ($self,$x,$y,$n,@r) = objectify(2,@_); | |
1787 | } | |
58cde26e JH |
1788 | |
1789 | return $x if $x->modify('brsft'); | |
1790 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
f9a08e12 JH |
1791 | return $x->round(@r) if $y->is_zero(); |
1792 | return $x->bzero(@r) if $x->is_zero(); # 0 => 0 | |
58cde26e JH |
1793 | |
1794 | $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-'; | |
574bacfe | 1795 | |
b3abae2a JH |
1796 | # this only works for negative numbers when shifting in base 2 |
1797 | if (($x->{sign} eq '-') && ($n == 2)) | |
1798 | { | |
f9a08e12 | 1799 | return $x->round(@r) if $x->is_one('-'); # -1 => -1 |
b3abae2a JH |
1800 | if (!$y->is_one()) |
1801 | { | |
1802 | # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al | |
1803 | # but perhaps there is a better emulation for two's complement shift... | |
1804 | # if $y != 1, we must simulate it by doing: | |
1805 | # convert to bin, flip all bits, shift, and be done | |
1806 | $x->binc(); # -3 => -2 | |
1807 | my $bin = $x->as_bin(); | |
1808 | $bin =~ s/^-0b//; # strip '-0b' prefix | |
1809 | $bin =~ tr/10/01/; # flip bits | |
1810 | # now shift | |
8f675a64 | 1811 | if (CORE::length($bin) <= $y) |
b3abae2a JH |
1812 | { |
1813 | $bin = '0'; # shifting to far right creates -1 | |
1814 | # 0, because later increment makes | |
1815 | # that 1, attached '-' makes it '-1' | |
1816 | # because -1 >> x == -1 ! | |
1817 | } | |
1818 | else | |
1819 | { | |
1820 | $bin =~ s/.{$y}$//; # cut off at the right side | |
1821 | $bin = '1' . $bin; # extend left side by one dummy '1' | |
1822 | $bin =~ tr/10/01/; # flip bits back | |
1823 | } | |
1824 | my $res = $self->new('0b'.$bin); # add prefix and convert back | |
1825 | $res->binc(); # remember to increment | |
1826 | $x->{value} = $res->{value}; # take over value | |
f9a08e12 | 1827 | return $x->round(@r); # we are done now, magic, isn't? |
b3abae2a | 1828 | } |
b282a552 | 1829 | # x < 0, n == 2, y == 1 |
b3abae2a JH |
1830 | $x->bdec(); # n == 2, but $y == 1: this fixes it |
1831 | } | |
1832 | ||
9b924220 RGS |
1833 | $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n); |
1834 | $x->round(@r); | |
58cde26e JH |
1835 | } |
1836 | ||
1837 | sub band | |
1838 | { | |
1839 | #(BINT or num_str, BINT or num_str) return BINT | |
1840 | # compute x & y | |
f9a08e12 JH |
1841 | |
1842 | # set up parameters | |
1843 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1844 | # objectify is costly, so avoid it | |
1845 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1846 | { | |
1847 | ($self,$x,$y,@r) = objectify(2,@_); | |
1848 | } | |
58cde26e JH |
1849 | |
1850 | return $x if $x->modify('band'); | |
1851 | ||
f9a08e12 | 1852 | $r[3] = $y; # no push! |
b3abae2a | 1853 | |
58cde26e | 1854 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
0716bf9b | 1855 | |
b282a552 T |
1856 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
1857 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe | 1858 | |
9b924220 | 1859 | if ($sx == 1 && $sy == 1) |
0716bf9b | 1860 | { |
574bacfe | 1861 | $x->{value} = $CALC->_and($x->{value},$y->{value}); |
f9a08e12 | 1862 | return $x->round(@r); |
0716bf9b | 1863 | } |
091c87b1 T |
1864 | |
1865 | if ($CAN{signed_and}) | |
1866 | { | |
1867 | $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy); | |
1868 | return $x->round(@r); | |
1869 | } | |
b282a552 T |
1870 | |
1871 | require $EMU_LIB; | |
1872 | __emu_band($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
1873 | } |
1874 | ||
1875 | sub bior | |
1876 | { | |
1877 | #(BINT or num_str, BINT or num_str) return BINT | |
1878 | # compute x | y | |
f9a08e12 JH |
1879 | |
1880 | # set up parameters | |
1881 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1882 | # objectify is costly, so avoid it | |
1883 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1884 | { | |
1885 | ($self,$x,$y,@r) = objectify(2,@_); | |
1886 | } | |
58cde26e JH |
1887 | |
1888 | return $x if $x->modify('bior'); | |
f9a08e12 | 1889 | $r[3] = $y; # no push! |
58cde26e JH |
1890 | |
1891 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); | |
574bacfe | 1892 | |
b282a552 T |
1893 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
1894 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe | 1895 | |
091c87b1 T |
1896 | # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior() |
1897 | ||
574bacfe | 1898 | # don't use lib for negative values |
9b924220 | 1899 | if ($sx == 1 && $sy == 1) |
0716bf9b | 1900 | { |
574bacfe | 1901 | $x->{value} = $CALC->_or($x->{value},$y->{value}); |
f9a08e12 | 1902 | return $x->round(@r); |
0716bf9b JH |
1903 | } |
1904 | ||
b282a552 | 1905 | # if lib can do negative values, let it handle this |
091c87b1 T |
1906 | if ($CAN{signed_or}) |
1907 | { | |
1908 | $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy); | |
1909 | return $x->round(@r); | |
1910 | } | |
1911 | ||
b282a552 T |
1912 | require $EMU_LIB; |
1913 | __emu_bior($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
1914 | } |
1915 | ||
1916 | sub bxor | |
1917 | { | |
1918 | #(BINT or num_str, BINT or num_str) return BINT | |
1919 | # compute x ^ y | |
f9a08e12 JH |
1920 | |
1921 | # set up parameters | |
1922 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
1923 | # objectify is costly, so avoid it | |
1924 | if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) | |
1925 | { | |
1926 | ($self,$x,$y,@r) = objectify(2,@_); | |
1927 | } | |
58cde26e JH |
1928 | |
1929 | return $x if $x->modify('bxor'); | |
f9a08e12 | 1930 | $r[3] = $y; # no push! |
58cde26e | 1931 | |
0716bf9b | 1932 | return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); |
0716bf9b | 1933 | |
b282a552 T |
1934 | my $sx = $x->{sign} eq '+' ? 1 : -1; |
1935 | my $sy = $y->{sign} eq '+' ? 1 : -1; | |
574bacfe JH |
1936 | |
1937 | # don't use lib for negative values | |
9b924220 | 1938 | if ($sx == 1 && $sy == 1) |
0716bf9b | 1939 | { |
574bacfe | 1940 | $x->{value} = $CALC->_xor($x->{value},$y->{value}); |
f9a08e12 | 1941 | return $x->round(@r); |
0716bf9b | 1942 | } |
091c87b1 | 1943 | |
b282a552 | 1944 | # if lib can do negative values, let it handle this |
091c87b1 T |
1945 | if ($CAN{signed_xor}) |
1946 | { | |
1947 | $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy); | |
1948 | return $x->round(@r); | |
1949 | } | |
0716bf9b | 1950 | |
b282a552 T |
1951 | require $EMU_LIB; |
1952 | __emu_bxor($self,$x,$y,$sx,$sy,@r); | |
58cde26e JH |
1953 | } |
1954 | ||
1955 | sub length | |
1956 | { | |
b282a552 | 1957 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 1958 | |
0716bf9b | 1959 | my $e = $CALC->_len($x->{value}); |
091c87b1 | 1960 | wantarray ? ($e,0) : $e; |
58cde26e JH |
1961 | } |
1962 | ||
1963 | sub digit | |
1964 | { | |
0716bf9b | 1965 | # return the nth decimal digit, negative values count backward, 0 is right |
ef9466ea | 1966 | my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_); |
58cde26e | 1967 | |
ef9466ea | 1968 | $n = $n->numify() if ref($n); |
f9a08e12 | 1969 | $CALC->_digit($x->{value},$n||0); |
58cde26e JH |
1970 | } |
1971 | ||
1972 | sub _trailing_zeros | |
1973 | { | |
b282a552 | 1974 | # return the amount of trailing zeros in $x (as scalar) |
58cde26e JH |
1975 | my $x = shift; |
1976 | $x = $class->new($x) unless ref $x; | |
1977 | ||
9b924220 | 1978 | return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc |
0716bf9b | 1979 | |
9b924220 | 1980 | $CALC->_zeros($x->{value}); # must handle odd values, 0 etc |
58cde26e JH |
1981 | } |
1982 | ||
1983 | sub bsqrt | |
1984 | { | |
990fb837 | 1985 | # calculate square root of $x |
f9a08e12 | 1986 | my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_); |
58cde26e | 1987 | |
b3abae2a JH |
1988 | return $x if $x->modify('bsqrt'); |
1989 | ||
990fb837 RGS |
1990 | return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN |
1991 | return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf | |
b3abae2a | 1992 | |
f9a08e12 | 1993 | return $upgrade->bsqrt($x,@r) if defined $upgrade; |
58cde26e | 1994 | |
9b924220 RGS |
1995 | $x->{value} = $CALC->_sqrt($x->{value}); |
1996 | $x->round(@r); | |
58cde26e JH |
1997 | } |
1998 | ||
990fb837 RGS |
1999 | sub broot |
2000 | { | |
2001 | # calculate $y'th root of $x | |
c38b2de2 | 2002 | |
990fb837 RGS |
2003 | # set up parameters |
2004 | my ($self,$x,$y,@r) = (ref($_[0]),@_); | |
c38b2de2 JH |
2005 | |
2006 | $y = $self->new(2) unless defined $y; | |
2007 | ||
990fb837 | 2008 | # objectify is costly, so avoid it |
c38b2de2 | 2009 | if ((!ref($x)) || (ref($x) ne ref($y))) |
990fb837 | 2010 | { |
3a427a11 | 2011 | ($self,$x,$y,@r) = objectify(2,$self || $class,@_); |
990fb837 RGS |
2012 | } |
2013 | ||
2014 | return $x if $x->modify('broot'); | |
2015 | ||
2016 | # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 | |
2017 | return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || | |
2018 | $y->{sign} !~ /^\+$/; | |
2019 | ||
2020 | return $x->round(@r) | |
2021 | if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); | |
2022 | ||
c38b2de2 | 2023 | return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade; |
990fb837 | 2024 | |
9b924220 RGS |
2025 | $x->{value} = $CALC->_root($x->{value},$y->{value}); |
2026 | $x->round(@r); | |
990fb837 RGS |
2027 | } |
2028 | ||
58cde26e JH |
2029 | sub exponent |
2030 | { | |
2031 | # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) | |
ee15d750 | 2032 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); |
58cde26e | 2033 | |
ee15d750 JH |
2034 | if ($x->{sign} !~ /^[+-]$/) |
2035 | { | |
b282a552 T |
2036 | my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf |
2037 | return $self->new($s); | |
ee15d750 | 2038 | } |
b282a552 T |
2039 | return $self->bone() if $x->is_zero(); |
2040 | ||
2041 | $self->new($x->_trailing_zeros()); | |
58cde26e JH |
2042 | } |
2043 | ||
2044 | sub mantissa | |
2045 | { | |
ee15d750 JH |
2046 | # return the mantissa (compatible to Math::BigFloat, e.g. reduced) |
2047 | my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); | |
58cde26e | 2048 | |
ee15d750 JH |
2049 | if ($x->{sign} !~ /^[+-]$/) |
2050 | { | |
b282a552 T |
2051 | # for NaN, +inf, -inf: keep the sign |
2052 | return $self->new($x->{sign}); | |
ee15d750 | 2053 | } |
b282a552 T |
2054 | my $m = $x->copy(); delete $m->{_p}; delete $m->{_a}; |
2055 | # that's a bit inefficient: | |
58cde26e | 2056 | my $zeros = $m->_trailing_zeros(); |
56b9c951 | 2057 | $m->brsft($zeros,10) if $zeros != 0; |
56b9c951 | 2058 | $m; |
58cde26e JH |
2059 | } |
2060 | ||
2061 | sub parts | |
2062 | { | |
ee15d750 | 2063 | # return a copy of both the exponent and the mantissa |
091c87b1 | 2064 | my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); |
58cde26e | 2065 | |
091c87b1 | 2066 | ($x->mantissa(),$x->exponent()); |
58cde26e JH |
2067 | } |
2068 | ||
2069 | ############################################################################## | |
2070 | # rounding functions | |
2071 | ||
2072 | sub bfround | |
2073 | { | |
2074 | # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' | |
ee15d750 | 2075 | # $n == 0 || $n == 1 => round to integer |
ef9466ea | 2076 | my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x; |
b282a552 | 2077 | |
dccbb853 | 2078 | my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_); |
b282a552 T |
2079 | |
2080 | return $x if !defined $scale || $x->modify('bfround'); # no-op | |
58cde26e JH |
2081 | |
2082 | # no-op for BigInts if $n <= 0 | |
b282a552 | 2083 | $x->bround( $x->length()-$scale, $mode) if $scale > 0; |
58cde26e | 2084 | |
ef9466ea T |
2085 | delete $x->{_a}; # delete to save memory |
2086 | $x->{_p} = $scale; # store new _p | |
ee15d750 | 2087 | $x; |
58cde26e JH |
2088 | } |
2089 | ||
2090 | sub _scan_for_nonzero | |
2091 | { | |
ae161977 RGS |
2092 | # internal, used by bround() to scan for non-zeros after a '5' |
2093 | my ($x,$pad,$xs,$len) = @_; | |
58cde26e | 2094 | |
ae161977 | 2095 | return 0 if $len == 1; # "5" is trailed by invisible zeros |
58cde26e JH |
2096 | my $follow = $pad - 1; |
2097 | return 0 if $follow > $len || $follow < 1; | |
0716bf9b | 2098 | |
ae161977 RGS |
2099 | # use the string form to check whether only '0's follow or not |
2100 | substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0; | |
58cde26e JH |
2101 | } |
2102 | ||
2103 | sub fround | |
2104 | { | |
091c87b1 T |
2105 | # Exists to make life easier for switch between MBF and MBI (should we |
2106 | # autoload fxxx() like MBF does for bxxx()?) | |
58cde26e | 2107 | my $x = shift; |
091c87b1 | 2108 | $x->bround(@_); |
58cde26e JH |
2109 | } |
2110 | ||
2111 | sub bround | |
2112 | { | |
2113 | # accuracy: +$n preserve $n digits from left, | |
2114 | # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) | |
2115 | # no-op for $n == 0 | |
2116 | # and overwrite the rest with 0's, return normalized number | |
2117 | # do not return $x->bnorm(), but $x | |
61f5c3f5 | 2118 | |
58cde26e | 2119 | my $x = shift; $x = $class->new($x) unless ref $x; |
dccbb853 | 2120 | my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_); |
61f5c3f5 | 2121 | return $x if !defined $scale; # no-op |
b3abae2a | 2122 | return $x if $x->modify('bround'); |
58cde26e | 2123 | |
61f5c3f5 T |
2124 | if ($x->is_zero() || $scale == 0) |
2125 | { | |
2126 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 | |
2127 | return $x; | |
2128 | } | |
2129 | return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN | |
58cde26e JH |
2130 | |
2131 | # we have fewer digits than we want to scale to | |
2132 | my $len = $x->length(); | |
56d9de68 T |
2133 | # convert $scale to a scalar in case it is an object (put's a limit on the |
2134 | # number length, but this would already limited by memory constraints), makes | |
2135 | # it faster | |
2136 | $scale = $scale->numify() if ref ($scale); | |
2137 | ||
ee15d750 JH |
2138 | # scale < 0, but > -len (not >=!) |
2139 | if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) | |
2140 | { | |
61f5c3f5 | 2141 | $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 |
ee15d750 JH |
2142 | return $x; |
2143 | } | |
58cde26e JH |
2144 | |
2145 | # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 | |
2146 | my ($pad,$digit_round,$digit_after); | |
2147 | $pad = $len - $scale; | |
ee15d750 JH |
2148 | $pad = abs($scale-1) if $scale < 0; |
2149 | ||
ae161977 RGS |
2150 | # do not use digit(), it is very costly for binary => decimal |
2151 | # getting the entire string is also costly, but we need to do it only once | |
0716bf9b JH |
2152 | my $xs = $CALC->_str($x->{value}); |
2153 | my $pl = -$pad-1; | |
56d9de68 | 2154 | |
0716bf9b JH |
2155 | # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 |
2156 | # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 | |
9b924220 | 2157 | $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len; |
0716bf9b | 2158 | $pl++; $pl ++ if $pad >= $len; |
9b924220 | 2159 | $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0; |
ee15d750 | 2160 | |
58cde26e JH |
2161 | # in case of 01234 we round down, for 6789 up, and only in case 5 we look |
2162 | # closer at the remaining digits of the original $x, remember decision | |
2163 | my $round_up = 1; # default round up | |
2164 | $round_up -- if | |
2165 | ($mode eq 'trunc') || # trunc by round down | |
2166 | ($digit_after =~ /[01234]/) || # round down anyway, | |
2167 | # 6789 => round up | |
2168 | ($digit_after eq '5') && # not 5000...0000 | |
ae161977 | 2169 | ($x->_scan_for_nonzero($pad,$xs,$len) == 0) && |
58cde26e JH |
2170 | ( |
2171 | ($mode eq 'even') && ($digit_round =~ /[24680]/) || | |
2172 | ($mode eq 'odd') && ($digit_round =~ /[13579]/) || | |
2173 | ($mode eq '+inf') && ($x->{sign} eq '-') || | |
2174 | ($mode eq '-inf') && ($x->{sign} eq '+') || | |
2175 | ($mode eq 'zero') # round down if zero, sign adjusted below | |
2176 | ); | |
61f5c3f5 T |
2177 | my $put_back = 0; # not yet modified |
2178 | ||
61f5c3f5 T |
2179 | if (($pad > 0) && ($pad <= $len)) |
2180 | { | |
ae161977 RGS |
2181 | substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...' |
2182 | $put_back = 1; # need to put back | |
58cde26e | 2183 | } |
61f5c3f5 T |
2184 | elsif ($pad > $len) |
2185 | { | |
2186 | $x->bzero(); # round to '0' | |
2187 | } | |
2188 | ||
58cde26e JH |
2189 | if ($round_up) # what gave test above? |
2190 | { | |
ae161977 | 2191 | $put_back = 1; # need to put back |
9b924220 | 2192 | $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0 |
61f5c3f5 T |
2193 | |
2194 | # we modify directly the string variant instead of creating a number and | |
f9a08e12 | 2195 | # adding it, since that is faster (we already have the string) |
61f5c3f5 T |
2196 | my $c = 0; $pad ++; # for $pad == $len case |
2197 | while ($pad <= $len) | |
2198 | { | |
9b924220 RGS |
2199 | $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10'; |
2200 | substr($xs,-$pad,1) = $c; $pad++; | |
61f5c3f5 T |
2201 | last if $c != 0; # no overflow => early out |
2202 | } | |
9b924220 | 2203 | $xs = '1'.$xs if $c == 0; |
61f5c3f5 | 2204 | |
58cde26e | 2205 | } |
ae161977 | 2206 | $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed |
ee15d750 JH |
2207 | |
2208 | $x->{_a} = $scale if $scale >= 0; | |
2209 | if ($scale < 0) | |
2210 | { | |
2211 | $x->{_a} = $len+$scale; | |
2212 | $x->{_a} = 0 if $scale < -$len; | |
2213 | } | |
58cde26e JH |
2214 | $x; |
2215 | } | |
2216 | ||
2217 | sub bfloor | |
2218 | { | |
091c87b1 T |
2219 | # return integer less or equal then number; no-op since it's already integer |
2220 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
58cde26e | 2221 | |
f9a08e12 | 2222 | $x->round(@r); |
58cde26e JH |
2223 | } |
2224 | ||
2225 | sub bceil | |
2226 | { | |
091c87b1 T |
2227 | # return integer greater or equal then number; no-op since it's already int |
2228 | my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); | |
58cde26e | 2229 | |
f9a08e12 | 2230 | $x->round(@r); |
58cde26e JH |
2231 | } |
2232 | ||
091c87b1 T |
2233 | sub as_number |
2234 | { | |
2235 | # An object might be asked to return itself as bigint on certain overloaded | |
2236 | # operations, this does exactly this, so that sub classes can simple inherit | |
2237 | # it or override with their own integer conversion routine. | |
2238 | $_[0]->copy(); | |
2239 | } | |
58cde26e | 2240 | |
091c87b1 | 2241 | sub as_hex |
58cde26e | 2242 | { |
091c87b1 T |
2243 | # return as hex string, with prefixed 0x |
2244 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2245 | ||
2246 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2247 | ||
b282a552 | 2248 | my $s = ''; |
091c87b1 | 2249 | $s = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 2250 | $s . $CALC->_as_hex($x->{value}); |
58cde26e JH |
2251 | } |
2252 | ||
091c87b1 | 2253 | sub as_bin |
58cde26e | 2254 | { |
091c87b1 T |
2255 | # return as binary string, with prefixed 0b |
2256 | my $x = shift; $x = $class->new($x) if !ref($x); | |
2257 | ||
2258 | return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc | |
2259 | ||
b282a552 | 2260 | my $s = ''; $s = $x->{sign} if $x->{sign} eq '-'; |
9b924220 | 2261 | return $s . $CALC->_as_bin($x->{value}); |
58cde26e JH |
2262 | } |
2263 | ||
091c87b1 T |
2264 | ############################################################################## |
2265 | # private stuff (internal use only) | |
2266 | ||
58cde26e JH |
2267 | sub objectify |
2268 | { | |
2269 | # check for strings, if yes, return objects instead | |
2270 | ||
2271 | # the first argument is number of args objectify() should look at it will | |
2272 | # return $count+1 elements, the first will be a classname. This is because | |
2273 | # overloaded '""' calls bstr($object,undef,undef) and this would result in | |
2274 | # useless objects beeing created and thrown away. So we cannot simple loop | |
2275 | # over @_. If the given count is 0, all arguments will be used. | |
2276 | ||
2277 | # If the second arg is a ref, use it as class. | |
2278 | # If not, try to use it as classname, unless undef, then use $class | |
2279 | # (aka Math::BigInt). The latter shouldn't happen,though. | |
2280 | ||
2281 | # caller: gives us: | |
2282 | # $x->badd(1); => ref x, scalar y | |
2283 | # Class->badd(1,2); => classname x (scalar), scalar x, scalar y | |
2284 | # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y | |
2285 | # Math::BigInt::badd(1,2); => scalar x, scalar y | |
2286 | # In the last case we check number of arguments to turn it silently into | |
574bacfe | 2287 | # $class,1,2. (We can not take '1' as class ;o) |
58cde26e JH |
2288 | # badd($class,1) is not supported (it should, eventually, try to add undef) |
2289 | # currently it tries 'Math::BigInt' + 1, which will not work. | |
ee15d750 JH |
2290 | |
2291 | # some shortcut for the common cases | |
ee15d750 JH |
2292 | # $x->unary_op(); |
2293 | return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); | |
ee15d750 | 2294 | |
58cde26e JH |
2295 | my $count = abs(shift || 0); |
2296 | ||
9393ace2 | 2297 | my (@a,$k,$d); # resulting array, temp, and downgrade |
58cde26e JH |
2298 | if (ref $_[0]) |
2299 | { | |
2300 | # okay, got object as first | |
2301 | $a[0] = ref $_[0]; | |
2302 | } | |
2303 | else | |
2304 | { | |
2305 | # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) | |
2306 | $a[0] = $class; | |
58cde26e JH |
2307 | $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? |
2308 | } | |
8f675a64 | 2309 | |
9393ace2 JH |
2310 | no strict 'refs'; |
2311 | # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats | |
2312 | if (defined ${"$a[0]::downgrade"}) | |
2313 | { | |
2314 | $d = ${"$a[0]::downgrade"}; | |
2315 | ${"$a[0]::downgrade"} = undef; | |
2316 | } | |
2317 | ||
d614cd8b | 2318 | my $up = ${"$a[0]::upgrade"}; |
c38b2de2 | 2319 | #print "Now in objectify, my class is today $a[0], count = $count\n"; |
58cde26e JH |
2320 | if ($count == 0) |
2321 | { | |
2322 | while (@_) | |
2323 | { | |
2324 | $k = shift; | |
2325 | if (!ref($k)) | |
2326 | { | |
2327 | $k = $a[0]->new($k); | |
2328 | } | |
d614cd8b | 2329 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2330 | { |
2331 | # foreign object, try to convert to integer | |
2332 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2333 | } |
58cde26e JH |
2334 | push @a,$k; |
2335 | } | |
2336 | } | |
2337 | else | |
2338 | { | |
2339 | while ($count > 0) | |
2340 | { | |
58cde26e JH |
2341 | $count--; |
2342 | $k = shift; | |
2343 | if (!ref($k)) | |
2344 | { | |
2345 | $k = $a[0]->new($k); | |
2346 | } | |
d614cd8b | 2347 | elsif (!defined $up && ref($k) ne $a[0]) |
58cde26e JH |
2348 | { |
2349 | # foreign object, try to convert to integer | |
2350 | $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); | |
e16b8f49 | 2351 | } |
58cde26e JH |
2352 | push @a,$k; |
2353 | } | |
2354 | push @a,@_; # return other params, too | |
2355 | } | |
990fb837 RGS |
2356 | if (! wantarray) |
2357 | { | |
2358 | require Carp; Carp::croak ("$class objectify needs list context"); | |
2359 | } | |
9393ace2 | 2360 | ${"$a[0]::downgrade"} = $d; |
58cde26e JH |
2361 | @a; |
2362 | } | |
2363 | ||
2364 | sub import | |
2365 | { | |
2366 | my $self = shift; | |
61f5c3f5 | 2367 | |
091c87b1 | 2368 | $IMPORT++; # remember we did import() |
8f675a64 JH |
2369 | my @a; my $l = scalar @_; |
2370 | for ( my $i = 0; $i < $l ; $i++ ) | |
58cde26e | 2371 | { |
0716bf9b | 2372 | if ($_[$i] eq ':constant') |
58cde26e | 2373 | { |
0716bf9b | 2374 | # this causes overlord er load to step in |
091c87b1 T |
2375 | overload::constant |
2376 | integer => sub { $self->new(shift) }, | |
2377 | binary => sub { $self->new(shift) }; | |
0716bf9b | 2378 | } |
b3abae2a JH |
2379 | elsif ($_[$i] eq 'upgrade') |
2380 | { | |
2381 | # this causes upgrading | |
2382 | $upgrade = $_[$i+1]; # or undef to disable | |
8f675a64 | 2383 | $i++; |
b3abae2a | 2384 | } |
0716bf9b JH |
2385 | elsif ($_[$i] =~ /^lib$/i) |
2386 | { | |
2387 | # this causes a different low lib to take care... | |
61f5c3f5 | 2388 | $CALC = $_[$i+1] || ''; |
8f675a64 JH |
2389 | $i++; |
2390 | } | |
2391 | else | |
2392 | { | |
2393 | push @a, $_[$i]; | |
58cde26e JH |
2394 | } |
2395 | } | |
2396 | # any non :constant stuff is handled by our parent, Exporter | |
2397 | # even if @_ is empty, to give it a chance | |
dccbb853 JH |
2398 | $self->SUPER::import(@a); # need it for subclasses |
2399 | $self->export_to_level(1,$self,@a); # need it for MBF | |
58cde26e | 2400 | |
574bacfe JH |
2401 | # try to load core math lib |
2402 | my @c = split /\s*,\s*/,$CALC; | |
2403 | push @c,'Calc'; # if all fail, try this | |
61f5c3f5 | 2404 | $CALC = ''; # signal error |
574bacfe JH |
2405 | foreach my $lib (@c) |
2406 | { | |
07d34614 | 2407 | next if ($lib || '') eq ''; |
574bacfe JH |
2408 | $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; |
2409 | $lib =~ s/\.pm$//; | |
61f5c3f5 | 2410 | if ($] < 5.006) |
574bacfe JH |
2411 | { |
2412 | # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is | |
2413 | # used in the same script, or eval inside import(). | |
07d34614 T |
2414 | my @parts = split /::/, $lib; # Math::BigInt => Math BigInt |
2415 | my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm | |
2416 | require File::Spec; | |
2417 | $file = File::Spec->catfile (@parts, $file); | |
2418 | eval { require "$file"; $lib->import( @c ); } | |
574bacfe JH |
2419 | } |
2420 | else | |
2421 | { | |
61f5c3f5 | 2422 | eval "use $lib qw/@c/;"; |
574bacfe | 2423 | } |
9b924220 RGS |
2424 | if ($@ eq '') |
2425 | { | |
2426 | my $ok = 1; | |
2427 | # loaded it ok, see if the api_version() is high enough | |
2428 | if ($lib->can('api_version') && $lib->api_version() >= 1.0) | |
2429 | { | |
2430 | $ok = 0; | |
2431 | # api_version matches, check if it really provides anything we need | |
2432 | for my $method (qw/ | |
2433 | one two ten | |
2434 | str num | |
2435 | add mul div sub dec inc | |
2436 | acmp len digit is_one is_zero is_even is_odd | |
2437 | is_two is_ten | |
2438 | new copy check from_hex from_bin as_hex as_bin zeros | |
2439 | rsft lsft xor and or | |
2440 | mod sqrt root fac pow modinv modpow log_int gcd | |
2441 | /) | |
2442 | { | |
2443 | if (!$lib->can("_$method")) | |
2444 | { | |
2445 | if (($WARN{$lib}||0) < 2) | |
2446 | { | |
2447 | require Carp; | |
2448 | Carp::carp ("$lib is missing method '_$method'"); | |
2449 | $WARN{$lib} = 1; # still warn about the lib | |
2450 | } | |
2451 | $ok++; last; | |
2452 | } | |
2453 | } | |
2454 | } | |
2455 | if ($ok == 0) | |
2456 | { | |
2457 | $CALC = $lib; | |
2458 | last; # found a usable one, break | |
2459 | } | |
2460 | else | |
2461 | { | |
2462 | if (($WARN{$lib}||0) < 2) | |
2463 | { | |
2464 | my $ver = eval "\$$lib\::VERSION"; | |
2465 | require Carp; | |
2466 | Carp::carp ("Cannot load outdated $lib v$ver, please upgrade"); | |
2467 | $WARN{$lib} = 2; # never warn again | |
2468 | } | |
2469 | } | |
2470 | } | |
574bacfe | 2471 | } |
990fb837 RGS |
2472 | if ($CALC eq '') |
2473 | { | |
2474 | require Carp; | |
091c87b1 T |
2475 | Carp::croak ("Couldn't load any math lib, not even 'Calc.pm'"); |
2476 | } | |
9b924220 | 2477 | _fill_can_cache(); # for emulating lower math lib functions |
091c87b1 T |
2478 | } |
2479 | ||
2480 | sub _fill_can_cache | |
2481 | { | |
2482 | # fill $CAN with the results of $CALC->can(...) | |
2483 | ||
2484 | %CAN = (); | |
9b924220 | 2485 | for my $method (qw/ signed_and or signed_or xor signed_xor /) |
091c87b1 T |
2486 | { |
2487 | $CAN{$method} = $CALC->can("_$method") ? 1 : 0; | |
990fb837 | 2488 | } |
58cde26e JH |
2489 | } |
2490 | ||
574bacfe | 2491 | sub __from_hex |
58cde26e JH |
2492 | { |
2493 | # convert a (ref to) big hex string to BigInt, return undef for error | |
2494 | my $hs = shift; | |
2495 | ||
2496 | my $x = Math::BigInt->bzero(); | |
394e6ffb JH |
2497 | |
2498 | # strip underscores | |
9b924220 RGS |
2499 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; |
2500 | $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g; | |
394e6ffb | 2501 | |
9b924220 | 2502 | return $x->bnan() if $hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/; |
58cde26e | 2503 | |
9b924220 | 2504 | my $sign = '+'; $sign = '-' if $hs =~ /^-/; |
58cde26e | 2505 | |
9b924220 RGS |
2506 | $hs =~ s/^[+-]//; # strip sign |
2507 | $x->{value} = $CALC->_from_hex($hs); | |
13a12e00 JH |
2508 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2509 | $x; | |
58cde26e JH |
2510 | } |
2511 | ||
574bacfe | 2512 | sub __from_bin |
58cde26e JH |
2513 | { |
2514 | # convert a (ref to) big binary string to BigInt, return undef for error | |
2515 | my $bs = shift; | |
2516 | ||
2517 | my $x = Math::BigInt->bzero(); | |
394e6ffb | 2518 | # strip underscores |
9b924220 RGS |
2519 | $bs =~ s/([01])_([01])/$1$2/g; |
2520 | $bs =~ s/([01])_([01])/$1$2/g; | |
2521 | return $x->bnan() if $bs !~ /^[+-]?0b[01]+$/; | |
58cde26e | 2522 | |
9b924220 RGS |
2523 | my $sign = '+'; $sign = '-' if $bs =~ /^\-/; |
2524 | $bs =~ s/^[+-]//; # strip sign | |
2525 | ||
2526 | $x->{value} = $CALC->_from_bin($bs); | |
13a12e00 JH |
2527 | $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0' |
2528 | $x; | |
58cde26e JH |
2529 | } |
2530 | ||
2531 | sub _split | |
2532 | { | |
2533 | # (ref to num_str) return num_str | |
2534 | # internal, take apart a string and return the pieces | |
dccbb853 | 2535 | # strip leading/trailing whitespace, leading zeros, underscore and reject |
574bacfe | 2536 | # invalid input |
58cde26e JH |
2537 | my $x = shift; |
2538 | ||
574bacfe | 2539 | # strip white space at front, also extranous leading zeros |
9b924220 RGS |
2540 | $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' |
2541 | $x =~ s/^\s+//; # but this will | |
2542 | $x =~ s/\s+$//g; # strip white space at end | |
58cde26e | 2543 | |
574bacfe | 2544 | # shortcut, if nothing to split, return early |
9b924220 | 2545 | if ($x =~ /^[+-]?\d+\z/) |
574bacfe | 2546 | { |
9b924220 RGS |
2547 | $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; |
2548 | return (\$sign, \$x, \'', \'', \0); | |
574bacfe | 2549 | } |
58cde26e | 2550 | |
574bacfe | 2551 | # invalid starting char? |
9b924220 | 2552 | return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; |
58cde26e | 2553 | |
9b924220 RGS |
2554 | return __from_hex($x) if $x =~ /^[\-\+]?0x/; # hex string |
2555 | return __from_bin($x) if $x =~ /^[\-\+]?0b/; # binary string | |
394e6ffb JH |
2556 | |
2557 | # strip underscores between digits | |
9b924220 RGS |
2558 | $x =~ s/(\d)_(\d)/$1$2/g; |
2559 | $x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3 | |
574bacfe | 2560 | |
58cde26e JH |
2561 | # some possible inputs: |
2562 | # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 | |
aef458a0 | 2563 | # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999 |
58cde26e | 2564 | |
9b924220 | 2565 | my ($m,$e,$last) = split /[Ee]/,$x; |
56d9de68 | 2566 | return if defined $last; # last defined => 1e2E3 or others |
58cde26e | 2567 | $e = '0' if !defined $e || $e eq ""; |
56d9de68 | 2568 | |
58cde26e JH |
2569 | # sign,value for exponent,mantint,mantfrac |
2570 | my ($es,$ev,$mis,$miv,$mfv); | |
2571 | # valid exponent? | |
2572 | if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2573 | { | |
2574 | $es = $1; $ev = $2; | |
58cde26e JH |
2575 | # valid mantissa? |
2576 | return if $m eq '.' || $m eq ''; | |
56d9de68 | 2577 | my ($mi,$mf,$lastf) = split /\./,$m; |
8df1e0a2 | 2578 | return if defined $lastf; # lastf defined => 1.2.3 or others |
58cde26e JH |
2579 | $mi = '0' if !defined $mi; |
2580 | $mi .= '0' if $mi =~ /^[\-\+]?$/; | |
2581 | $mf = '0' if !defined $mf || $mf eq ''; | |
2582 | if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros | |
2583 | { | |
2584 | $mis = $1||'+'; $miv = $2; | |
58cde26e JH |
2585 | return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros |
2586 | $mfv = $1; | |
aef458a0 JH |
2587 | # handle the 0e999 case here |
2588 | $ev = 0 if $miv eq '0' && $mfv eq ''; | |
58cde26e JH |
2589 | return (\$mis,\$miv,\$mfv,\$es,\$ev); |
2590 | } | |
2591 | } | |
2592 | return; # NaN, not a number | |
2593 | } | |
2594 | ||
58cde26e | 2595 | ############################################################################## |
0716bf9b | 2596 | # internal calculation routines (others are in Math::BigInt::Calc etc) |
58cde26e | 2597 | |
dccbb853 | 2598 | sub __lcm |
58cde26e JH |
2599 | { |
2600 | # (BINT or num_str, BINT or num_str) return BINT | |
2601 | # does modify first argument | |
2602 | # LCM | |
2603 | ||
2604 | my $x = shift; my $ty = shift; | |
2605 | return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan); | |
9b924220 | 2606 | $x * $ty / bgcd($x,$ty); |
58cde26e JH |
2607 | } |
2608 | ||
58cde26e JH |
2609 | ############################################################################### |
2610 | # this method return 0 if the object can be modified, or 1 for not | |
b282a552 | 2611 | # We use a fast constant sub() here, to avoid costly calls. Subclasses |
58cde26e JH |
2612 | # may override it with special code (f.i. Math::BigInt::Constant does so) |
2613 | ||
0716bf9b | 2614 | sub modify () { 0; } |
e16b8f49 | 2615 | |
a0d0e21e | 2616 | 1; |
a5f75d66 AD |
2617 | __END__ |
2618 | ||
2619 | =head1 NAME | |
2620 | ||
2621 | Math::BigInt - Arbitrary size integer math package | |
2622 | ||
2623 | =head1 SYNOPSIS | |
2624 | ||
2625 | use Math::BigInt; | |
58cde26e | 2626 | |
990fb837 RGS |
2627 | # or make it faster: install (optional) Math::BigInt::GMP |
2628 | # and always use (it will fall back to pure Perl if the | |
2629 | # GMP library is not installed): | |
2630 | ||
2631 | use Math::BigInt lib => 'GMP'; | |
2632 | ||
9b924220 RGS |
2633 | my $str = '1234567890'; |
2634 | my @values = (64,74,18); | |
2635 | my $n = 1; my $sign = '-'; | |
2636 | ||
58cde26e | 2637 | # Number creation |
574bacfe | 2638 | $x = Math::BigInt->new($str); # defaults to 0 |
9b924220 | 2639 | $y = $x->copy(); # make a true copy |
574bacfe JH |
2640 | $nan = Math::BigInt->bnan(); # create a NotANumber |
2641 | $zero = Math::BigInt->bzero(); # create a +0 | |
2642 | $inf = Math::BigInt->binf(); # create a +inf | |
2643 | $inf = Math::BigInt->binf('-'); # create a -inf | |
2644 | $one = Math::BigInt->bone(); # create a +1 | |
2645 | $one = Math::BigInt->bone('-'); # create a -1 | |
58cde26e | 2646 | |
56d9de68 T |
2647 | # Testing (don't modify their arguments) |
2648 | # (return true if the condition is met, otherwise false) | |
2649 | ||
2650 | $x->is_zero(); # if $x is +0 | |
2651 | $x->is_nan(); # if $x is NaN | |
2652 | $x->is_one(); # if $x is +1 | |
2653 | $x->is_one('-'); # if $x is -1 | |
2654 | $x->is_odd(); # if $x is odd | |
2655 | $x->is_even(); # if $x is even | |
b282a552 T |
2656 | $x->is_pos(); # if $x >= 0 |
2657 | $x->is_neg(); # if $x < 0 | |
9b924220 | 2658 | $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+') |
56d9de68 T |
2659 | $x->is_int(); # if $x is an integer (not a float) |
2660 | ||
2661 | # comparing and digit/sign extration | |
2662 | $x->bcmp($y); # compare numbers (undef,<0,=0,>0) | |
2663 | $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) | |
2664 | $x->sign(); # return the sign, either +,- or NaN | |
2665 | $x->digit($n); # return the nth digit, counting from right | |
2666 | $x->digit(-$n); # return the nth digit, counting from left | |
58cde26e | 2667 | |
990fb837 RGS |
2668 | # The following all modify their first argument. If you want to preserve |
2669 | # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is | |
2670 | # neccessary when mixing $a = $b assigments with non-overloaded math. | |
58cde26e | 2671 | |
56d9de68 T |
2672 | $x->bzero(); # set $x to 0 |
2673 | $x->bnan(); # set $x to NaN | |
2674 | $x->bone(); # set $x to +1 | |
2675 | $x->bone('-'); # set $x to -1 | |
2676 | $x->binf(); # set $x to inf | |
2677 | $x->binf('-'); # set $x to -inf | |
2678 | ||
2679 | $x->bneg(); # negation | |
2680 | $x->babs(); # absolute value | |
2681 | $x->bnorm(); # normalize (no-op in BigInt) | |
2682 | $x->bnot(); # two's complement (bit wise not) | |
2683 | $x->binc(); # increment $x by 1 | |
2684 | $x->bdec(); # decrement $x by 1 | |
58cde26e | 2685 | |
56d9de68 T |
2686 | $x->badd($y); # addition (add $y to $x) |
2687 | $x->bsub($y); # subtraction (subtract $y from $x) | |
2688 | $x->bmul($y); # multiplication (multiply $x by $y) | |
2689 | $x->bdiv($y); # divide, set $x to quotient | |
2690 | # return (quo,rem) or quo if scalar | |
2691 | ||
2692 | $x->bmod($y); # modulus (x % y) | |
2693 | $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod)) | |
2694 | $x->bmodinv($mod); # the inverse of $x in the given modulus $mod | |
2695 | ||
2696 | $x->bpow($y); # power of arguments (x ** y) | |
2697 | $x->blsft($y); # left shift | |
2698 | $x->brsft($y); # right shift | |
2699 | $x->blsft($y,$n); # left shift, by base $n (like 10) | |
2700 | $x->brsft($y,$n); # right shift, by base $n (like 10) | |
58cde26e | 2701 | |
56d9de68 T |
2702 | $x->band($y); # bitwise and |
2703 | $x->bior($y); # bitwise inclusive or | |
2704 | $x->bxor($y); # bitwise exclusive or | |
2705 | $x->bnot(); # bitwise not (two's complement) | |
2706 | ||
2707 | $x->bsqrt(); # calculate square-root | |
990fb837 | 2708 | $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) |
56d9de68 | 2709 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
58cde26e | 2710 | |
990fb837 | 2711 | $x->round($A,$P,$mode); # round to accuracy or precision using mode $mode |
9b924220 RGS |
2712 | $x->bround($n); # accuracy: preserve $n digits |
2713 | $x->bfround($n); # round to $nth digit, no-op for BigInts | |
58cde26e | 2714 | |
990fb837 | 2715 | # The following do not modify their arguments in BigInt (are no-ops), |
56d9de68 | 2716 | # but do so in BigFloat: |
58cde26e | 2717 | |
56d9de68 T |
2718 | $x->bfloor(); # return integer less or equal than $x |
2719 | $x->bceil(); # return integer greater or equal than $x | |
58cde26e JH |
2720 | |
2721 | # The following do not modify their arguments: | |
2722 | ||
9b924220 RGS |
2723 | # greatest common divisor (no OO style) |
2724 | my $gcd = Math::BigInt::bgcd(@values); | |
2725 | # lowest common multiplicator (no OO style) | |
2726 | my $lcm = Math::BigInt::blcm(@values); | |
bd05a461 | 2727 | |
56d9de68 | 2728 | $x->length(); # return number of digits in number |
9b924220 | 2729 | ($xl,$f) = $x->length(); # length of number and length of fraction part, |
56d9de68 T |
2730 | # latter is always 0 digits long for BigInt's |
2731 | ||
2732 | $x->exponent(); # return exponent as BigInt | |
2733 | $x->mantissa(); # return (signed) mantissa as BigInt | |
2734 | $x->parts(); # return (mantissa,exponent) as BigInt | |
2735 | $x->copy(); # make a true copy of $x (unlike $y = $x;) | |
b282a552 T |
2736 | $x->as_int(); # return as BigInt (in BigInt: same as copy()) |
2737 | $x->numify(); # return as scalar (might overflow!) | |
bd05a461 | 2738 | |
56d9de68 T |
2739 | # conversation to string (do not modify their argument) |
2740 | $x->bstr(); # normalized string | |
2741 | $x->bsstr(); # normalized string in scientific notation | |
2742 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x | |
2743 | $x->as_bin(); # as signed binary string with prefixed 0b | |
b282a552 | 2744 | |
bd05a461 | 2745 | |
f9a08e12 | 2746 | # precision and accuracy (see section about rounding for more) |
56d9de68 T |
2747 | $x->precision(); # return P of $x (or global, if P of $x undef) |
2748 | $x->precision($n); # set P of $x to $n | |
2749 | $x->accuracy(); # return A of $x (or global, if A of $x undef) | |
2750 | $x->accuracy($n); # set A $x to $n | |
f9a08e12 | 2751 | |
56d9de68 T |
2752 | # Global methods |
2753 | Math::BigInt->precision(); # get/set global P for all BigInt objects | |
2754 | Math::BigInt->accuracy(); # get/set global A for all BigInt objects | |
2755 | Math::BigInt->config(); # return hash containing configuration | |
f9a08e12 | 2756 | |
a5f75d66 AD |
2757 | =head1 DESCRIPTION |
2758 | ||
58cde26e JH |
2759 | All operators (inlcuding basic math operations) are overloaded if you |
2760 | declare your big integers as | |
a5f75d66 | 2761 | |
58cde26e | 2762 | $i = new Math::BigInt '123_456_789_123_456_789'; |
a5f75d66 | 2763 | |
58cde26e JH |
2764 | Operations with overloaded operators preserve the arguments which is |
2765 | exactly what you expect. | |
a5f75d66 AD |
2766 | |
2767 | =over 2 | |
2768 | ||
aef458a0 | 2769 | =item Input |
a5f75d66 | 2770 | |
aef458a0 JH |
2771 | Input values to these routines may be any string, that looks like a number |
2772 | and results in an integer, including hexadecimal and binary numbers. | |
58cde26e | 2773 | |
aef458a0 JH |
2774 | Scalars holding numbers may also be passed, but note that non-integer numbers |
2775 | may already have lost precision due to the conversation to float. Quote | |
091c87b1 | 2776 | your input if you want BigInt to see all the digits: |
a5f75d66 | 2777 | |
aef458a0 JH |
2778 | $x = Math::BigInt->new(12345678890123456789); # bad |
2779 | $x = Math::BigInt->new('12345678901234567890'); # good | |
58cde26e | 2780 | |
56d9de68 | 2781 | You can include one underscore between any two digits. |
58cde26e JH |
2782 | |
2783 | This means integer values like 1.01E2 or even 1000E-2 are also accepted. | |
aef458a0 | 2784 | Non-integer values result in NaN. |
58cde26e | 2785 | |
aef458a0 | 2786 | Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('') |
091c87b1 T |
2787 | results in 'NaN'. This might change in the future, so use always the following |
2788 | explicit forms to get a zero or NaN: | |
2789 | ||
2790 | $zero = Math::BigInt->bzero(); | |
2791 | $nan = Math::BigInt->bnan(); | |
58cde26e | 2792 | |
aef458a0 | 2793 | C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers |
091c87b1 | 2794 | are always stored in normalized form. If passed a string, creates a BigInt |
aef458a0 | 2795 | object from the input. |
a5f75d66 AD |
2796 | |
2797 | =item Output | |
2798 | ||
58cde26e JH |
2799 | Output values are BigInt objects (normalized), except for bstr(), which |
2800 | returns a string in normalized form. | |
2801 | Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>, | |
2802 | C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>) | |
2803 | return either undef, <0, 0 or >0 and are suited for sort. | |
a5f75d66 AD |
2804 | |
2805 | =back | |
2806 | ||
b3abae2a JH |
2807 | =head1 METHODS |
2808 | ||
56d9de68 T |
2809 | Each of the methods below (except config(), accuracy() and precision()) |
2810 | accepts three additional parameters. These arguments $A, $P and $R are | |
2811 | accuracy, precision and round_mode. Please see the section about | |
2812 | L<ACCURACY and PRECISION> for more information. | |
b3abae2a | 2813 | |
8f675a64 JH |
2814 | =head2 config |
2815 | ||
2816 | use Data::Dumper; | |
2817 | ||
2818 | print Dumper ( Math::BigInt->config() ); | |
56d9de68 | 2819 | print Math::BigInt->config()->{lib},"\n"; |
8f675a64 JH |
2820 | |
2821 | Returns a hash containing the configuration, e.g. the version number, lib | |
56d9de68 T |
2822 | loaded etc. The following hash keys are currently filled in with the |
2823 | appropriate information. | |
2824 | ||
2825 | key Description | |
2826 | Example | |
2827 | ============================================================ | |
091c87b1 | 2828 | lib Name of the low-level math library |
56d9de68 | 2829 | Math::BigInt::Calc |
091c87b1 | 2830 | lib_version Version of low-level math library (see 'lib') |
56d9de68 | 2831 | 0.30 |
091c87b1 | 2832 | class The class name of config() you just called |
56d9de68 | 2833 | Math::BigInt |
091c87b1 | 2834 | upgrade To which class math operations might be upgraded |
56d9de68 | 2835 | Math::BigFloat |
091c87b1 | 2836 | downgrade To which class math operations might be downgraded |
56d9de68 T |
2837 | undef |
2838 | precision Global precision | |
2839 | undef | |
2840 | accuracy Global accuracy | |
2841 | undef | |
2842 | round_mode Global round mode | |
2843 | even | |
2844 | version version number of the class you used | |
2845 | 1.61 | |
2846 | div_scale Fallback acccuracy for div | |
2847 | 40 | |
091c87b1 T |
2848 | trap_nan If true, traps creation of NaN via croak() |
2849 | 1 | |
2850 | trap_inf If true, traps creation of +inf/-inf via croak() | |
2851 | 1 | |
56d9de68 | 2852 | |
c38b2de2 | 2853 | The following values can be set by passing C<config()> a reference to a hash: |
93c87d9d T |
2854 | |
2855 | trap_inf trap_nan | |
2856 | upgrade downgrade precision accuracy round_mode div_scale | |
2857 | ||
2858 | Example: | |
2859 | ||
2860 | $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } ); | |
8f675a64 | 2861 | |
13a12e00 JH |
2862 | =head2 accuracy |
2863 | ||
2864 | $x->accuracy(5); # local for $x | |
56d9de68 T |
2865 | CLASS->accuracy(5); # global for all members of CLASS |
2866 | $A = $x->accuracy(); # read out | |
2867 | $A = CLASS->accuracy(); # read out | |
13a12e00 JH |
2868 | |
2869 | Set or get the global or local accuracy, aka how many significant digits the | |
56d9de68 T |
2870 | results have. |
2871 | ||
2872 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
13a12e00 JH |
2873 | |
2874 | Value must be greater than zero. Pass an undef value to disable it: | |
2875 | ||
2876 | $x->accuracy(undef); | |
2877 | Math::BigInt->accuracy(undef); | |
2878 | ||
2879 | Returns the current accuracy. For C<$x->accuracy()> it will return either the | |
2880 | local accuracy, or if not defined, the global. This means the return value | |
2881 | represents the accuracy that will be in effect for $x: | |
2882 | ||
2883 | $y = Math::BigInt->new(1234567); # unrounded | |
2884 | print Math::BigInt->accuracy(4),"\n"; # set 4, print 4 | |
2885 | $x = Math::BigInt->new(123456); # will be automatically rounded | |
2886 | print "$x $y\n"; # '123500 1234567' | |
2887 | print $x->accuracy(),"\n"; # will be 4 | |
2888 | print $y->accuracy(),"\n"; # also 4, since global is 4 | |
2889 | print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 | |
2890 | print $x->accuracy(),"\n"; # still 4 | |
2891 | print $y->accuracy(),"\n"; # 5, since global is 5 | |
2892 | ||
56d9de68 T |
2893 | Note: Works also for subclasses like Math::BigFloat. Each class has it's own |
2894 | globals separated from Math::BigInt, but it is possible to subclass | |
2895 | Math::BigInt and make the globals of the subclass aliases to the ones from | |
2896 | Math::BigInt. | |
2897 | ||
2898 | =head2 precision | |
2899 | ||
2900 | $x->precision(-2); # local for $x, round right of the dot | |
2901 | $x->precision(2); # ditto, but round left of the dot | |
2902 | CLASS->accuracy(5); # global for all members of CLASS | |
2903 | CLASS->precision(-5); # ditto | |
2904 | $P = CLASS->precision(); # read out | |
2905 | $P = $x->precision(); # read out | |
2906 | ||
2907 | Set or get the global or local precision, aka how many digits the result has | |
2908 | after the dot (or where to round it when passing a positive number). In | |
2909 | Math::BigInt, passing a negative number precision has no effect since no | |
2910 | numbers have digits after the dot. | |
2911 | ||
2912 | Please see the section about L<ACCURACY AND PRECISION> for further details. | |
2913 | ||
2914 | Value must be greater than zero. Pass an undef value to disable it: | |
2915 | ||
2916 | $x->precision(undef); | |
2917 | Math::BigInt->precision(undef); | |
2918 | ||
2919 | Returns the current precision. For C<$x->precision()> it will return either the | |
2920 | local precision of $x, or if not defined, the global. This means the return | |
2921 | value represents the accuracy that will be in effect for $x: | |
2922 | ||
2923 | $y = Math::BigInt->new(1234567); # unrounded | |
2924 | print Math::BigInt->precision(4),"\n"; # set 4, print 4 | |
2925 | $x = Math::BigInt->new(123456); # will be automatically rounded | |
2926 | ||
2927 | Note: Works also for subclasses like Math::BigFloat. Each class has it's own | |
2928 | globals separated from Math::BigInt, but it is possible to subclass | |
2929 | Math::BigInt and make the globals of the subclass aliases to the ones from | |
2930 | Math::BigInt. | |
2931 | ||
b3abae2a JH |
2932 | =head2 brsft |
2933 | ||
2934 | $x->brsft($y,$n); | |
2935 | ||
2936 | Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and | |
2937 | 2, but others work, too. | |
2938 | ||
2939 | Right shifting usually amounts to dividing $x by $n ** $y and truncating the | |
2940 | result: | |
2941 | ||
2942 | ||
2943 | $x = Math::BigInt->new(10); | |
2944 | $x->brsft(1); # same as $x >> 1: 5 | |
2945 | $x = Math::BigInt->new(1234); | |
2946 | $x->brsft(2,10); # result 12 | |
2947 | ||
2948 | There is one exception, and that is base 2 with negative $x: | |
2949 | ||
2950 | ||
2951 | $x = Math::BigInt->new(-5); | |
2952 | print $x->brsft(1); | |
2953 | ||
2954 | This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the | |
2955 | result). | |
2956 | ||
2957 | =head2 new | |
2958 | ||
2959 | $x = Math::BigInt->new($str,$A,$P,$R); | |
2960 | ||
aef458a0 | 2961 | Creates a new BigInt object from a scalar or another BigInt object. The |
b3abae2a JH |
2962 | input is accepted as decimal, hex (with leading '0x') or binary (with leading |
2963 | '0b'). | |
2964 | ||
aef458a0 JH |
2965 | See L<Input> for more info on accepted input formats. |
2966 | ||
b3abae2a JH |
2967 | =head2 bnan |
2968 | ||
2969 | $x = Math::BigInt->bnan(); | |
2970 | ||
2971 | Creates a new BigInt object representing NaN (Not A Number). | |
2972 | If used on an object, it will set it to NaN: | |
2973 | ||
2974 | $x->bnan(); | |
2975 | ||
2976 | =head2 bzero | |
2977 | ||
2978 | $x = Math::BigInt->bzero(); | |
2979 | ||
2980 | Creates a new BigInt object representing zero. | |
2981 | If used on an object, it will set it to zero: | |
2982 | ||
2983 | $x->bzero(); | |
2984 | ||
2985 | =head2 binf | |
2986 | ||
2987 | $x = Math::BigInt->binf($sign); | |
2988 | ||
2989 | Creates a new BigInt object representing infinity. The optional argument is | |
2990 | either '-' or '+', indicating whether you want infinity or minus infinity. | |
2991 | If used on an object, it will set it to infinity: | |
2992 | ||
2993 | $x->binf(); | |
2994 | $x->binf('-'); | |
2995 | ||
2996 | =head2 bone | |
2997 | ||
2998 | $x = Math::BigInt->binf($sign); | |
2999 | ||
3000 | Creates a new BigInt object representing one. The optional argument is | |
3001 | either '-' or '+', indicating whether you want one or minus one. | |
3002 | If used on an object, it will set it to one: | |
3003 | ||
3004 | $x->bone(); # +1 | |
3005 | $x->bone('-'); # -1 | |
3006 | ||
56b9c951 JH |
3007 | =head2 is_one()/is_zero()/is_nan()/is_inf() |
3008 | ||
b3abae2a JH |
3009 | |
3010 | $x->is_zero(); # true if arg is +0 | |
3011 | $x->is_nan(); # true if arg is NaN | |
3012 | $x->is_one(); # true if arg is +1 | |
3013 | $x->is_one('-'); # true if arg is -1 | |
b3abae2a JH |
3014 | $x->is_inf(); # true if +inf |
3015 | $x->is_inf('-'); # true if -inf (sign is default '+') | |
56b9c951 JH |
3016 | |
3017 | These methods all test the BigInt for beeing one specific value and return | |
3018 | true or false depending on the input. These are faster than doing something | |
3019 | like: | |
3020 | ||
3021 | if ($x == 0) | |
3022 | ||
b282a552 | 3023 | =head2 is_pos()/is_neg() |
56b9c951 | 3024 | |
b282a552 T |
3025 | $x->is_pos(); # true if >= 0 |
3026 | $x->is_neg(); # true if < 0 | |
56b9c951 JH |
3027 | |
3028 | The methods return true if the argument is positive or negative, respectively. | |
3029 | C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and | |
3030 | C<-inf> is negative. A C<zero> is positive. | |
3031 | ||
3032 | These methods are only testing the sign, and not the value. | |
3033 | ||
b282a552 T |
3034 | C<is_positive()> and C<is_negative()> are aliase to C<is_pos()> and |
3035 | C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were | |
3036 | introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced | |
3037 | in v1.68. | |
3038 | ||
56b9c951 JH |
3039 | =head2 is_odd()/is_even()/is_int() |
3040 | ||
3041 | $x->is_odd(); # true if odd, false for even | |
3042 | $x->is_even(); # true if even, false for odd | |
b3abae2a JH |
3043 | $x->is_int(); # true if $x is an integer |
3044 | ||
56b9c951 JH |
3045 | The return true when the argument satisfies the condition. C<NaN>, C<+inf>, |
3046 | C<-inf> are not integers and are neither odd nor even. | |
b3abae2a | 3047 | |
c38b2de2 JH |
3048 | In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers. |
3049 | ||
b3abae2a JH |
3050 | =head2 bcmp |
3051 | ||
56b9c951 JH |
3052 | $x->bcmp($y); |
3053 | ||
3054 | Compares $x with $y and takes the sign into account. | |
3055 | Returns -1, 0, 1 or undef. | |
b3abae2a JH |
3056 | |
3057 | =head2 bacmp | |
3058 | ||
56b9c951 JH |
3059 | $x->bacmp($y); |
3060 | ||
3061 | Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef. | |
b3abae2a JH |
3062 | |
3063 | =head2 sign | |
3064 | ||
56b9c951 JH |
3065 | $x->sign(); |
3066 | ||
3067 | Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. | |
b3abae2a | 3068 | |
091c87b1 T |
3069 | =head2 digit |
3070 | ||
3071 | $x->digit($n); # return the nth digit, counting from right | |
b3abae2a | 3072 | |
091c87b1 | 3073 | If C<$n> is negative, returns the digit counting from left. |
b3abae2a JH |
3074 | |
3075 | =head2 bneg | |
3076 | ||
3077 | $x->bneg(); | |
3078 | ||
3079 | Negate the number, e.g. change the sign between '+' and '-', or between '+inf' | |
3080 | and '-inf', respectively. Does nothing for NaN or zero. | |
3081 | ||
3082 | =head2 babs | |
3083 | ||
3084 | $x->babs(); | |
3085 | ||
3086 | Set the number to it's absolute value, e.g. change the sign from '-' to '+' | |
3087 | and from '-inf' to '+inf', respectively. Does nothing for NaN or positive | |
3088 | numbers. | |
3089 | ||
3090 | =head2 bnorm | |
3091 | ||
56d9de68 | 3092 | $x->bnorm(); # normalize (no-op) |
b3abae2a JH |
3093 | |
3094 | =head2 bnot | |
3095 | ||
091c87b1 T |
3096 | $x->bnot(); |
3097 | ||
3098 | Two's complement (bit wise not). This is equivalent to | |
3099 | ||
3100 | $x->binc()->bneg(); | |
3101 | ||
3102 | but faster. | |
b3abae2a JH |
3103 | |
3104 | =head2 binc | |
3105 | ||
56d9de68 | 3106 | $x->binc(); # increment x by 1 |
b3abae2a JH |
3107 | |
3108 | =head2 bdec | |
3109 | ||
56d9de68 | 3110 | $x->bdec(); # decrement x by 1 |
b3abae2a JH |
3111 | |
3112 | =head2 badd | |
3113 | ||
56d9de68 | 3114 | $x->badd($y); # addition (add $y to $x) |
b3abae2a JH |
3115 | |
3116 | =head2 bsub | |
3117 | ||
56d9de68 | 3118 | $x->bsub($y); # subtraction (subtract $y from $x) |
b3abae2a JH |
3119 | |
3120 | =head2 bmul | |
3121 | ||
56d9de68 | 3122 | $x->bmul($y); # multiplication (multiply $x by $y) |
b3abae2a JH |
3123 | |
3124 | =head2 bdiv | |
3125 | ||
56d9de68 T |
3126 | $x->bdiv($y); # divide, set $x to quotient |
3127 | # return (quo,rem) or quo if scalar | |
b3abae2a JH |
3128 | |
3129 | =head2 bmod | |
3130 | ||
56d9de68 | 3131 | $x->bmod($y); # modulus (x % y) |
b3abae2a | 3132 | |
d614cd8b JH |
3133 | =head2 bmodinv |
3134 | ||
56d9de68 | 3135 | num->bmodinv($mod); # modular inverse |
d614cd8b JH |
3136 | |
3137 | Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is | |
3138 | returned unless C<$num> is relatively prime to C<$mod>, i.e. unless | |
3139 | C<bgcd($num, $mod)==1>. | |
3140 | ||
3141 | =head2 bmodpow | |
3142 | ||
56d9de68 T |
3143 | $num->bmodpow($exp,$mod); # modular exponentation |
3144 | # ($num**$exp % $mod) | |
d614cd8b JH |
3145 | |
3146 | Returns the value of C<$num> taken to the power C<$exp> in the modulus | |
3147 | C<$mod> using binary exponentation. C<bmodpow> is far superior to | |
3148 | writing | |
3149 | ||
56d9de68 | 3150 | $num ** $exp % $mod |
d614cd8b | 3151 | |
091c87b1 | 3152 | because it is much faster - it reduces internal variables into |
d614cd8b JH |
3153 | the modulus whenever possible, so it operates on smaller numbers. |
3154 | ||
3155 | C<bmodpow> also supports negative exponents. | |
3156 | ||
56d9de68 | 3157 | bmodpow($num, -1, $mod) |
d614cd8b JH |
3158 | |
3159 | is exactly equivalent to | |
3160 | ||
56d9de68 | 3161 | bmodinv($num, $mod) |
d614cd8b | 3162 | |
b3abae2a JH |
3163 | =head2 bpow |
3164 | ||
56d9de68 | 3165 | $x->bpow($y); # power of arguments (x ** y) |
b3abae2a JH |
3166 | |
3167 | =head2 blsft | |
3168 | ||
56d9de68 T |
3169 | $x->blsft($y); # left shift |
3170 | $x->blsft($y,$n); # left shift, in base $n (like 10) | |
b3abae2a JH |
3171 | |
3172 | =head2 brsft | |
3173 | ||
56d9de68 T |
3174 | $x->brsft($y); # right shift |
3175 | $x->brsft($y,$n); # right shift, in base $n (like 10) | |
b3abae2a JH |
3176 | |
3177 | =head2 band | |
3178 | ||
56d9de68 | 3179 | $x->band($y); # bitwise and |
b3abae2a JH |
3180 | |
3181 | =head2 bior | |
3182 | ||
56d9de68 | 3183 | $x->bior($y); # bitwise inclusive or |
b3abae2a JH |
3184 | |
3185 | =head2 bxor | |
3186 | ||
56d9de68 | 3187 | $x->bxor($y); # bitwise exclusive or |
b3abae2a JH |
3188 | |
3189 | =head2 bnot | |
3190 | ||
56d9de68 | 3191 | $x->bnot(); # bitwise not (two's complement) |
b3abae2a JH |
3192 | |
3193 | =head2 bsqrt | |
3194 | ||
56d9de68 | 3195 | $x->bsqrt(); # calculate square-root |
b3abae2a JH |
3196 | |
3197 | =head2 bfac | |
3198 | ||
56d9de68 | 3199 | $x->bfac(); # factorial of $x (1*2*3*4*..$x) |
b3abae2a JH |
3200 | |
3201 | =head2 round | |
3202 | ||
56d9de68 T |
3203 | $x->round($A,$P,$round_mode); |
3204 | ||
3205 | Round $x to accuracy C<$A> or precision C<$P> using the round mode | |
3206 | C<$round_mode>. | |
b3abae2a JH |
3207 | |
3208 | =head2 bround | |
3209 | ||
56d9de68 | 3210 | $x->bround($N); # accuracy: preserve $N digits |
b3abae2a JH |
3211 | |
3212 | =head2 bfround | |
3213 | ||
56d9de68 | 3214 | $x->bfround($N); # round to $Nth digit, no-op for BigInts |
b3abae2a JH |
3215 | |
3216 | =head2 bfloor | |
3217 | ||
3218 | $x->bfloor(); | |
3219 | ||
3220 | Set $x to the integer less or equal than $x. This is a no-op in BigInt, but | |
3221 | does change $x in BigFloat. | |
3222 | ||
3223 | =head2 bceil | |
3224 | ||
3225 | $x->bceil(); | |
3226 | ||
3227 | Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but | |
3228 | does change $x in BigFloat. | |
3229 | ||
3230 | =head2 bgcd | |
3231 | ||
56d9de68 | 3232 | bgcd(@values); # greatest common divisor (no OO style) |
b3abae2a JH |
3233 | |
3234 | =head2 blcm | |
3235 | ||
56d9de68 | 3236 | blcm(@values); # lowest common multiplicator (no OO style) |
b3abae2a JH |
3237 | |
3238 | head2 length | |
3239 | ||
3240 | $x->length(); | |
3241 | ($xl,$fl) = $x->length(); | |
3242 | ||
3243 | Returns the number of digits in the decimal representation of the number. | |
3244 | In list context, returns the length of the integer and fraction part. For | |
3245 | BigInt's, the length of the fraction part will always be 0. | |
3246 | ||
3247 | =head2 exponent | |
3248 | ||
3249 | $x->exponent(); | |
3250 | ||
3251 | Return the exponent of $x as BigInt. | |
3252 | ||
3253 | =head2 mantissa | |
3254 | ||
3255 | $x->mantissa(); | |
3256 | ||
3257 | Return the signed mantissa of $x as BigInt. | |
3258 | ||
3259 | =head2 parts | |
3260 | ||
56d9de68 | 3261 | $x->parts(); # return (mantissa,exponent) as BigInt |
b3abae2a JH |
3262 | |
3263 | =head2 copy | |
3264 | ||
56d9de68 | 3265 | $x->copy(); # make a true copy of $x (unlike $y = $x;) |
b3abae2a | 3266 | |
b282a552 | 3267 | =head2 as_int |
b3abae2a | 3268 | |
b282a552 T |
3269 | $x->as_int(); |
3270 | ||
3271 | Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as | |
3272 | C<copy()>. | |
3273 | ||
3274 | C<as_number()> is an alias to this method. C<as_number> was introduced in | |
3275 | v1.22, while C<as_int()> was only introduced in v1.68. | |
b3abae2a | 3276 | |
b282a552 T |
3277 | =head2 bstr |
3278 | ||
3279 | $x->bstr(); | |
b3abae2a | 3280 | |
b282a552 | 3281 | Returns a normalized string represantation of C<$x>. |
b3abae2a JH |
3282 | |
3283 | =head2 bsstr | |
3284 | ||
56d9de68 | 3285 | $x->bsstr(); # normalized string in scientific notation |
b3abae2a JH |
3286 | |
3287 | =head2 as_hex | |
3288 | ||
56d9de68 | 3289 | $x->as_hex(); # as signed hexadecimal string with prefixed 0x |
b3abae2a JH |
3290 | |
3291 | =head2 as_bin | |
3292 | ||
56d9de68 | 3293 | $x->as_bin(); # as signed binary string with prefixed 0b |
b3abae2a | 3294 | |
0716bf9b JH |
3295 | =head1 ACCURACY and PRECISION |
3296 | ||
b22b3e31 | 3297 | Since version v1.33, Math::BigInt and Math::BigFloat have full support for |
0716bf9b | 3298 | accuracy and precision based rounding, both automatically after every |
091c87b1 | 3299 | operation, as well as manually. |
0716bf9b JH |
3300 | |
3301 | This section describes the accuracy/precision handling in Math::Big* as it | |
b22b3e31 | 3302 | used to be and as it is now, complete with an explanation of all terms and |
0716bf9b JH |
3303 | abbreviations. |
3304 | ||
3305 | Not yet implemented things (but with correct description) are marked with '!', | |
3306 | things that need to be answered are marked with '?'. | |
3307 | ||
3308 | In the next paragraph follows a short description of terms used here (because | |
574bacfe | 3309 | these may differ from terms used by others people or documentation). |
0716bf9b | 3310 | |
b22b3e31 | 3311 | During the rest of this document, the shortcuts A (for accuracy), P (for |
0716bf9b JH |
3312 | precision), F (fallback) and R (rounding mode) will be used. |
3313 | ||
3314 | =head2 Precision P | |
3315 | ||
3316 | A fixed number of digits before (positive) or after (negative) | |
b22b3e31 PN |
3317 | the decimal point. For example, 123.45 has a precision of -2. 0 means an |
3318 | integer like 123 (or 120). A precision of 2 means two digits to the left | |
3319 | of the decimal point are zero, so 123 with P = 1 becomes 120. Note that | |
3320 | numbers with zeros before the decimal point may have different precisions, | |
3321 | because 1200 can have p = 0, 1 or 2 (depending on what the inital value | |
3322 | was). It could also have p < 0, when the digits after the decimal point | |
3323 | are zero. | |
0716bf9b | 3324 | |
574bacfe JH |
3325 | The string output (of floating point numbers) will be padded with zeros: |
3326 | ||
3327 | Initial value P A Result String | |
3328 | ------------------------------------------------------------ | |
3329 | 1234.01 -3 1000 1000 | |
3330 | 1234 -2 1200 1200 | |
3331 | 1234.5 -1 1230 1230 | |
3332 | 1234.001 1 1234 1234.0 | |
3333 | 1234.01 0 1234 1234 | |
3334 | 1234.01 2 1234.01 1234.01 | |
3335 | 1234.01 5 1234.01 1234.01000 | |
3336 | ||
3337 | For BigInts, no padding occurs. | |
0716bf9b JH |
3338 | |
3339 | =head2 Accuracy A | |
3340 | ||
3341 | Number of significant digits. Leading zeros are not counted. A | |
3342 | number may have an accuracy greater than the non-zero digits | |
b22b3e31 PN |
3343 | when there are zeros in it or trailing zeros. For example, 123.456 has |
3344 | A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3. | |
0716bf9b | 3345 | |
574bacfe JH |
3346 | The string output (of floating point numbers) will be padded with zeros: |
3347 | ||
3348 | Initial value P A Result String | |
3349 | ------------------------------------------------------------ | |
3350 | 1234.01 3 1230 1230 | |
3351 | 1234.01 6 1234.01 1234.01 | |
3352 | 1234.1 8 1234.1 1234.1000 | |
3353 | ||
3354 | For BigInts, no padding occurs. | |
3355 | ||
0716bf9b | 3356 | =head2 Fallback F |
a5f75d66 | 3357 | |
574bacfe JH |
3358 | When both A and P are undefined, this is used as a fallback accuracy when |
3359 | dividing numbers. | |
0716bf9b JH |
3360 | |
3361 | =head2 Rounding mode R | |
3362 | ||
3363 | When rounding a number, different 'styles' or 'kinds' | |
3364 | of rounding are possible. (Note that random rounding, as in | |
3365 | Math::Round, is not implemented.) | |
58cde26e JH |
3366 | |
3367 | =over 2 | |
a5f75d66 | 3368 | |
0716bf9b JH |
3369 | =item 'trunc' |
3370 | ||
3371 | truncation invariably removes all digits following the | |
3372 | rounding place, replacing them with zeros. Thus, 987.65 rounded | |
b22b3e31 | 3373 | to tens (P=1) becomes 980, and rounded to the fourth sigdig |
0716bf9b | 3374 | becomes 987.6 (A=4). 123.456 rounded to the second place after the |
b22b3e31 | 3375 | decimal point (P=-2) becomes 123.46. |
0716bf9b JH |
3376 | |
3377 | All other implemented styles of rounding attempt to round to the | |
3378 | "nearest digit." If the digit D immediately to the right of the | |
3379 | rounding place (skipping the decimal point) is greater than 5, the | |
3380 | number is incremented at the rounding place (possibly causing a | |
3381 | cascade of incrementation): e.g. when rounding to units, 0.9 rounds | |
3382 | to 1, and -19.9 rounds to -20. If D < 5, the number is similarly | |
3383 | truncated at the rounding place: e.g. when rounding to units, 0.4 | |
3384 | rounds to 0, and -19.4 rounds to -19. | |
3385 | ||
3386 | However the results of other styles of rounding differ if the | |
3387 | digit immediately to the right of the rounding place (skipping the | |
3388 | decimal point) is 5 and if there are no digits, or no digits other | |
3389 | than 0, after that 5. In such cases: | |
3390 | ||
3391 | =item 'even' | |
3392 | ||
3393 | rounds the digit at the rounding place to 0, 2, 4, 6, or 8 | |
3394 | if it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3395 | becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. | |
3396 | ||
3397 | =item 'odd' | |
3398 | ||
3399 | rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if | |
3400 | it is not already. E.g., when rounding to the first sigdig, 0.45 | |
3401 | becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. | |
3402 | ||
3403 | =item '+inf' | |
3404 | ||
3405 | round to plus infinity, i.e. always round up. E.g., when | |
3406 | rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, | |
b22b3e31 | 3407 | and 0.4501 also becomes 0.5. |
0716bf9b JH |
3408 | |
3409 | =item '-inf' | |
3410 | ||
3411 | round to minus infinity, i.e. always round down. E.g., when | |
3412 | rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, | |
3413 | but 0.4501 becomes 0.5. | |
3414 | ||
3415 | =item 'zero' | |
3416 | ||
3417 | round to zero, i.e. positive numbers down, negative ones up. | |
3418 | E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 | |
3419 | becomes -0.5, but 0.4501 becomes 0.5. | |
3420 | ||
3421 | =back | |
3422 | ||
3423 | The handling of A & P in MBI/MBF (the old core code shipped with Perl | |
3424 | versions <= 5.7.2) is like this: | |
3425 | ||
3426 | =over 2 | |
a5f75d66 | 3427 | |
0716bf9b JH |
3428 | =item Precision |
3429 | ||
b22b3e31 PN |
3430 | * ffround($p) is able to round to $p number of digits after the decimal |
3431 | point | |
0716bf9b JH |
3432 | * otherwise P is unused |
3433 | ||
3434 | =item Accuracy (significant digits) | |
3435 | ||
3436 | * fround($a) rounds to $a significant digits | |
3437 | * only fdiv() and fsqrt() take A as (optional) paramater | |
b22b3e31 | 3438 | + other operations simply create the same number (fneg etc), or more (fmul) |
0716bf9b JH |
3439 | of digits |
3440 | + rounding/truncating is only done when explicitly calling one of fround | |
3441 | or ffround, and never for BigInt (not implemented) | |
b22b3e31 | 3442 | * fsqrt() simply hands its accuracy argument over to fdiv. |
0716bf9b JH |
3443 | * the documentation and the comment in the code indicate two different ways |
3444 | on how fdiv() determines the maximum number of digits it should calculate, | |
3445 | and the actual code does yet another thing | |
3446 | POD: | |
3447 | max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) | |
3448 | Comment: | |
3449 | result has at most max(scale, length(dividend), length(divisor)) digits | |
3450 | Actual code: | |
3451 | scale = max(scale, length(dividend)-1,length(divisor)-1); | |
3452 | scale += length(divisior) - length(dividend); | |
b22b3e31 | 3453 | So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). |
0716bf9b JH |
3454 | Actually, the 'difference' added to the scale is calculated from the |
3455 | number of "significant digits" in dividend and divisor, which is derived | |
3456 | by looking at the length of the mantissa. Which is wrong, since it includes | |
091c87b1 | 3457 | the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops |
0716bf9b JH |
3458 | again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange |
3459 | assumption that 124 has 3 significant digits, while 120/7 will get you | |
3460 | '17', not '17.1' since 120 is thought to have 2 significant digits. | |
dccbb853 | 3461 | The rounding after the division then uses the remainder and $y to determine |
0716bf9b | 3462 | wether it must round up or down. |
b22b3e31 PN |
3463 | ? I have no idea which is the right way. That's why I used a slightly more |
3464 | ? simple scheme and tweaked the few failing testcases to match it. | |
58cde26e | 3465 | |
0716bf9b | 3466 | =back |
5dc6f178 | 3467 | |
0716bf9b | 3468 | This is how it works now: |
5dc6f178 | 3469 | |
0716bf9b | 3470 | =over 2 |
5dc6f178 | 3471 | |
0716bf9b JH |
3472 | =item Setting/Accessing |
3473 | ||
091c87b1 T |
3474 | * You can set the A global via C<< Math::BigInt->accuracy() >> or |
3475 | C<< Math::BigFloat->accuracy() >> or whatever class you are using. | |
3476 | * You can also set P globally by using C<< Math::SomeClass->precision() >> | |
3477 | likewise. | |
0716bf9b | 3478 | * Globals are classwide, and not inherited by subclasses. |
091c87b1 T |
3479 | * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >> |
3480 | * to undefine P, use C<< Math::SomeClass->precision(undef); >> | |
3481 | * Setting C<< Math::SomeClass->accuracy() >> clears automatically | |
3482 | C<< Math::SomeClass->precision() >>, and vice versa. | |
0716bf9b | 3483 | * To be valid, A must be > 0, P can have any value. |
b22b3e31 PN |
3484 | * If P is negative, this means round to the P'th place to the right of the |
3485 | decimal point; positive values mean to the left of the decimal point. | |
3486 | P of 0 means round to integer. | |
091c87b1 T |
3487 | * to find out the current global A, use C<< Math::SomeClass->accuracy() >> |
3488 | * to find out the current global P, use C<< Math::SomeClass->precision() >> | |
3489 | * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local | |
3490 | setting of C<< $x >>. | |
3491 | * Please note that C<< $x->accuracy() >> respecive C<< $x->precision() >> | |
3492 | return eventually defined global A or P, when C<< $x >>'s A or P is not | |
3493 | set. | |
0716bf9b JH |
3494 | |
3495 | =item Creating numbers | |
3496 | ||
b3abae2a JH |
3497 | * When you create a number, you can give it's desired A or P via: |
3498 | $x = Math::BigInt->new($number,$A,$P); | |
3499 | * Only one of A or P can be defined, otherwise the result is NaN | |
3500 | * If no A or P is give ($x = Math::BigInt->new($number) form), then the | |
3501 | globals (if set) will be used. Thus changing the global defaults later on | |
b22b3e31 | 3502 | will not change the A or P of previously created numbers (i.e., A and P of |
b3abae2a JH |
3503 | $x will be what was in effect when $x was created) |
3504 | * If given undef for A and P, B<no> rounding will occur, and the globals will | |
3505 | B<not> be used. This is used by subclasses to create numbers without | |
3506 | suffering rounding in the parent. Thus a subclass is able to have it's own | |
3507 | globals enforced upon creation of a number by using | |
091c87b1 | 3508 | C<< $x = Math::BigInt->new($number,undef,undef) >>: |
b3abae2a | 3509 | |
990fb837 | 3510 | use Math::BigInt::SomeSubclass; |
b3abae2a JH |
3511 | use Math::BigInt; |
3512 | ||
3513 | Math::BigInt->accuracy(2); | |
3514 | Math::BigInt::SomeSubClass->accuracy(3); | |
3515 | $x = Math::BigInt::SomeSubClass->new(1234); | |
3516 | ||
3517 | $x is now 1230, and not 1200. A subclass might choose to implement | |
3518 | this otherwise, e.g. falling back to the parent's A and P. | |
0716bf9b JH |
3519 | |
3520 | =item Usage | |
3521 | ||
b22b3e31 | 3522 | * If A or P are enabled/defined, they are used to round the result of each |
0716bf9b | 3523 | operation according to the rules below |
b22b3e31 PN |
3524 | * Negative P is ignored in Math::BigInt, since BigInts never have digits |
3525 | after the decimal point | |
091c87b1 T |
3526 | * Math::BigFloat uses Math::BigInt internally, but setting A or P inside |
3527 | Math::BigInt as globals does not tamper with the parts of a BigFloat. | |
3528 | A flag is used to mark all Math::BigFloat numbers as 'never round'. | |
0716bf9b JH |
3529 | |
3530 | =item Precedence | |
3531 | ||
b22b3e31 | 3532 | * It only makes sense that a number has only one of A or P at a time. |
091c87b1 T |
3533 | If you set either A or P on one object, or globally, the other one will |
3534 | be automatically cleared. | |
b3abae2a JH |
3535 | * If two objects are involved in an operation, and one of them has A in |
3536 | effect, and the other P, this results in an error (NaN). | |
091c87b1 T |
3537 | * A takes precendence over P (Hint: A comes before P). |
3538 | If neither of them is defined, nothing is used, i.e. the result will have | |
3539 | as many digits as it can (with an exception for fdiv/fsqrt) and will not | |
3540 | be rounded. | |
b22b3e31 PN |
3541 | * There is another setting for fdiv() (and thus for fsqrt()). If neither of |
3542 | A or P is defined, fdiv() will use a fallback (F) of $div_scale digits. | |
3543 | If either the dividend's or the divisor's mantissa has more digits than | |
3544 | the value of F, the higher value will be used instead of F. | |
3545 | This is to limit the digits (A) of the result (just consider what would | |
3546 | happen with unlimited A and P in the case of 1/3 :-) | |
b3abae2a | 3547 | * fdiv will calculate (at least) 4 more digits than required (determined by |
0716bf9b | 3548 | A, P or F), and, if F is not used, round the result |
b22b3e31 | 3549 | (this will still fail in the case of a result like 0.12345000000001 with A |
574bacfe | 3550 | or P of 5, but this can not be helped - or can it?) |
091c87b1 | 3551 | * Thus you can have the math done by on Math::Big* class in two modi: |
0716bf9b JH |
3552 | + never round (this is the default): |
3553 | This is done by setting A and P to undef. No math operation | |
b22b3e31 | 3554 | will round the result, with fdiv() and fsqrt() as exceptions to guard |
0716bf9b | 3555 | against overflows. You must explicitely call bround(), bfround() or |
b22b3e31 PN |
3556 | round() (the latter with parameters). |
3557 | Note: Once you have rounded a number, the settings will 'stick' on it | |
3558 | and 'infect' all other numbers engaged in math operations with it, since | |
0716bf9b JH |
3559 | local settings have the highest precedence. So, to get SaferRound[tm], |
3560 | use a copy() before rounding like this: | |
3561 | ||
3562 | $x = Math::BigFloat->new(12.34); | |
3563 | $y = Math::BigFloat->new(98.76); | |
3564 | $z = $x * $y; # 1218.6984 | |
3565 | print $x->copy()->fround(3); # 12.3 (but A is now 3!) | |
3566 | $z = $x * $y; # still 1218.6984, without | |
3567 | # copy would have been 1210! | |
3568 | ||
3569 | + round after each op: | |
b22b3e31 PN |
3570 | After each single operation (except for testing like is_zero()), the |
3571 | method round() is called and the result is rounded appropriately. By | |
0716bf9b | 3572 | setting proper values for A and P, you can have all-the-same-A or |
b22b3e31 PN |
3573 | all-the-same-P modes. For example, Math::Currency might set A to undef, |
3574 | and P to -2, globally. | |
0716bf9b | 3575 | |
b22b3e31 PN |
3576 | ?Maybe an extra option that forbids local A & P settings would be in order, |
3577 | ?so that intermediate rounding does not 'poison' further math? | |
0716bf9b JH |
3578 | |
3579 | =item Overriding globals | |
3580 | ||
3581 | * you will be able to give A, P and R as an argument to all the calculation | |
b22b3e31 | 3582 | routines; the second parameter is A, the third one is P, and the fourth is |
b3abae2a | 3583 | R (shift right by one for binary operations like badd). P is used only if |
b22b3e31 PN |
3584 | the first parameter (A) is undefined. These three parameters override the |
3585 | globals in the order detailed as follows, i.e. the first defined value | |
0716bf9b | 3586 | wins: |
b22b3e31 | 3587 | (local: per object, global: global default, parameter: argument to sub) |
0716bf9b JH |
3588 | + parameter A |
3589 | + parameter P | |
3590 | + local A (if defined on both of the operands: smaller one is taken) | |
b3abae2a | 3591 | + local P (if defined on both of the operands: bigger one is taken) |
0716bf9b JH |
3592 | + global A |
3593 | + global P | |
3594 | + global F | |
b22b3e31 | 3595 | * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two |
0716bf9b JH |
3596 | arguments (A and P) instead of one |
3597 | ||
3598 | =item Local settings | |
3599 | ||
091c87b1 T |
3600 | * You can set A or P locally by using C<< $x->accuracy() >> or |
3601 | C<< $x->precision() >> | |
0716bf9b | 3602 | and thus force different A and P for different objects/numbers. |
b22b3e31 | 3603 | * Setting A or P this way immediately rounds $x to the new value. |
091c87b1 | 3604 | * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa. |
0716bf9b JH |
3605 | |
3606 | =item Rounding | |
3607 | ||
b22b3e31 | 3608 | * the rounding routines will use the respective global or local settings. |
0716bf9b JH |
3609 | fround()/bround() is for accuracy rounding, while ffround()/bfround() |
3610 | is for precision | |
3611 | * the two rounding functions take as the second parameter one of the | |
3612 | following rounding modes (R): | |
3613 | 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' | |
091c87b1 T |
3614 | * you can set/get the global R by using C<< Math::SomeClass->round_mode() >> |
3615 | or by setting C<< $Math::SomeClass::round_mode >> | |
3616 | * after each operation, C<< $result->round() >> is called, and the result may | |
b22b3e31 PN |
3617 | eventually be rounded (that is, if A or P were set either locally, |
3618 | globally or as parameter to the operation) | |
091c87b1 | 3619 | * to manually round a number, call C<< $x->round($A,$P,$round_mode); >> |
b22b3e31 | 3620 | this will round the number by using the appropriate rounding function |
0716bf9b | 3621 | and then normalize it. |
b22b3e31 | 3622 | * rounding modifies the local settings of the number: |
0716bf9b JH |
3623 | |
3624 | $x = Math::BigFloat->new(123.456); | |
3625 | $x->accuracy(5); | |
3626 | $x->bround(4); | |
3627 | ||
3628 | Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() | |
3629 | will be 4 from now on. | |
3630 | ||
3631 | =item Default values | |
3632 | ||
3633 | * R: 'even' | |
3634 | * F: 40 | |
3635 | * A: undef | |
3636 | * P: undef | |
3637 | ||
3638 | =item Remarks | |
3639 | ||
3640 | * The defaults are set up so that the new code gives the same results as | |
3641 | the old code (except in a few cases on fdiv): | |
3642 | + Both A and P are undefined and thus will not be used for rounding | |
3643 | after each operation. | |
3644 | + round() is thus a no-op, unless given extra parameters A and P | |
58cde26e JH |
3645 | |
3646 | =back | |
3647 | ||
0716bf9b JH |
3648 | =head1 INTERNALS |
3649 | ||
574bacfe JH |
3650 | The actual numbers are stored as unsigned big integers (with seperate sign). |
3651 | You should neither care about nor depend on the internal representation; it | |
3652 | might change without notice. Use only method calls like C<< $x->sign(); >> | |
3653 | instead relying on the internal hash keys like in C<< $x->{sign}; >>. | |
3654 | ||
3655 | =head2 MATH LIBRARY | |
58cde26e | 3656 | |
574bacfe | 3657 | Math with the numbers is done (by default) by a module called |
091c87b1 | 3658 | C<Math::BigInt::Calc>. This is equivalent to saying: |
574bacfe JH |
3659 | |
3660 | use Math::BigInt lib => 'Calc'; | |
58cde26e | 3661 | |
0716bf9b | 3662 | You can change this by using: |
58cde26e | 3663 | |
0716bf9b | 3664 | use Math::BigInt lib => 'BitVect'; |
58cde26e | 3665 | |
574bacfe JH |
3666 | The following would first try to find Math::BigInt::Foo, then |
3667 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
0716bf9b | 3668 | |
574bacfe | 3669 | use Math::BigInt lib => 'Foo,Math::BigInt::Bar'; |
58cde26e | 3670 | |
091c87b1 T |
3671 | Since Math::BigInt::GMP is in almost all cases faster than Calc (especially in |
3672 | cases involving really big numbers, where it is B<much> faster), and there is | |
3673 | no penalty if Math::BigInt::GMP is not installed, it is a good idea to always | |
3674 | use the following: | |
3675 | ||
3676 | use Math::BigInt lib => 'GMP'; | |
3677 | ||
3678 | Different low-level libraries use different formats to store the | |
3679 | numbers. You should not depend on the number having a specific format. | |
3680 | ||
3681 | See the respective math library module documentation for further details. | |
58cde26e | 3682 | |
574bacfe JH |
3683 | =head2 SIGN |
3684 | ||
3685 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. | |
3686 | ||
3687 | A sign of 'NaN' is used to represent the result when input arguments are not | |
3688 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
3689 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
3690 | '-inf' when dividing any negative number by 0. | |
58cde26e JH |
3691 | |
3692 | =head2 mantissa(), exponent() and parts() | |
3693 | ||
3694 | C<mantissa()> and C<exponent()> return the said parts of the BigInt such | |
3695 | that: | |
3696 | ||
3697 | $m = $x->mantissa(); | |
3698 | $e = $x->exponent(); | |
3699 | $y = $m * ( 10 ** $e ); | |
3700 | print "ok\n" if $x == $y; | |
3701 | ||
b22b3e31 PN |
3702 | C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them |
3703 | in one go. Both the returned mantissa and exponent have a sign. | |
58cde26e | 3704 | |
091c87b1 T |
3705 | Currently, for BigInts C<$e> is always 0, except for NaN, +inf and -inf, |
3706 | where it is C<NaN>; and for C<$x == 0>, where it is C<1> (to be compatible | |
3707 | with Math::BigFloat's internal representation of a zero as C<0E1>). | |
58cde26e | 3708 | |
091c87b1 T |
3709 | C<$m> is currently just a copy of the original number. The relation between |
3710 | C<$e> and C<$m> will stay always the same, though their real values might | |
3711 | change. | |
0716bf9b | 3712 | |
58cde26e JH |
3713 | =head1 EXAMPLES |
3714 | ||
394e6ffb | 3715 | use Math::BigInt; |
574bacfe JH |
3716 | |
3717 | sub bint { Math::BigInt->new(shift); } | |
3718 | ||
394e6ffb | 3719 | $x = Math::BigInt->bstr("1234") # string "1234" |
58cde26e | 3720 | $x = "$x"; # same as bstr() |
990fb837 RGS |
3721 | $x = Math::BigInt->bneg("1234"); # BigInt "-1234" |
3722 | $x = Math::BigInt->babs("-12345"); # BigInt "12345" | |
58cde26e JH |
3723 | $x = Math::BigInt->bnorm("-0 00"); # BigInt "0" |
3724 | $x = bint(1) + bint(2); # BigInt "3" | |
3725 | $x = bint(1) + "2"; # ditto (auto-BigIntify of "2") | |
3726 | $x = bint(1); # BigInt "1" | |
3727 | $x = $x + 5 / 2; # BigInt "3" | |
3728 | $x = $x ** 3; # BigInt "27" | |
3729 | $x *= 2; # BigInt "54" | |
394e6ffb | 3730 | $x = Math::BigInt->new(0); # BigInt "0" |
58cde26e JH |
3731 | $x--; # BigInt "-1" |
3732 | $x = Math::BigInt->badd(4,5) # BigInt "9" | |
58cde26e | 3733 | print $x->bsstr(); # 9e+0 |
a5f75d66 | 3734 | |
0716bf9b JH |
3735 | Examples for rounding: |
3736 | ||
3737 | use Math::BigFloat; | |
3738 | use Test; | |
3739 | ||
3740 | $x = Math::BigFloat->new(123.4567); | |
3741 | $y = Math::BigFloat->new(123.456789); | |
394e6ffb | 3742 | Math::BigFloat->accuracy(4); # no more A than 4 |
0716bf9b JH |
3743 | |
3744 | ok ($x->copy()->fround(),123.4); # even rounding | |
3745 | print $x->copy()->fround(),"\n"; # 123.4 | |
3746 | Math::BigFloat->round_mode('odd'); # round to odd | |
3747 | print $x->copy()->fround(),"\n"; # 123.5 | |
394e6ffb | 3748 | Math::BigFloat->accuracy(5); # no more A than 5 |
0716bf9b JH |
3749 | Math::BigFloat->round_mode('odd'); # round to odd |
3750 | print $x->copy()->fround(),"\n"; # 123.46 | |
3751 | $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4 | |
3752 | print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 | |
3753 | ||
394e6ffb JH |
3754 | Math::BigFloat->accuracy(undef); # A not important now |
3755 | Math::BigFloat->precision(2); # P important | |
3756 | print $x->copy()->bnorm(),"\n"; # 123.46 | |
3757 | print $x->copy()->fround(),"\n"; # 123.46 | |
0716bf9b | 3758 | |
bd05a461 JH |
3759 | Examples for converting: |
3760 | ||
3761 | my $x = Math::BigInt->new('0b1'.'01' x 123); | |
3762 | print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; | |
3763 | ||
b3ac6de7 IZ |
3764 | =head1 Autocreating constants |
3765 | ||
56b9c951 JH |
3766 | After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal |
3767 | and binary constants in the given scope are converted to C<Math::BigInt>. | |
3768 | This conversion happens at compile time. | |
b3ac6de7 | 3769 | |
b22b3e31 | 3770 | In particular, |
b3ac6de7 | 3771 | |
58cde26e JH |
3772 | perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' |
3773 | ||
56b9c951 | 3774 | prints the integer value of C<2**100>. Note that without conversion of |
0716bf9b | 3775 | constants the expression 2**100 will be calculated as perl scalar. |
58cde26e JH |
3776 | |
3777 | Please note that strings and floating point constants are not affected, | |
3778 | so that | |
3779 | ||
3780 | use Math::BigInt qw/:constant/; | |
3781 | ||
3782 | $x = 1234567890123456789012345678901234567890 | |
3783 | + 123456789123456789; | |
b22b3e31 | 3784 | $y = '1234567890123456789012345678901234567890' |
58cde26e | 3785 | + '123456789123456789'; |
b3ac6de7 | 3786 | |
b22b3e31 | 3787 | do not work. You need an explicit Math::BigInt->new() around one of the |
394e6ffb JH |
3788 | operands. You should also quote large constants to protect loss of precision: |
3789 | ||
990fb837 | 3790 | use Math::BigInt; |
394e6ffb JH |
3791 | |
3792 | $x = Math::BigInt->new('1234567889123456789123456789123456789'); | |
3793 | ||
3794 | Without the quotes Perl would convert the large number to a floating point | |
3795 | constant at compile time and then hand the result to BigInt, which results in | |
3796 | an truncated result or a NaN. | |
58cde26e | 3797 | |
56b9c951 JH |
3798 | This also applies to integers that look like floating point constants: |
3799 | ||
3800 | use Math::BigInt ':constant'; | |
3801 | ||
3802 | print ref(123e2),"\n"; | |
3803 | print ref(123.2e2),"\n"; | |
3804 | ||
3805 | will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat> | |
3806 | to get this to work. | |
3807 | ||
58cde26e JH |
3808 | =head1 PERFORMANCE |
3809 | ||
3810 | Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x | |
3811 | must be made in the second case. For long numbers, the copy can eat up to 20% | |
b22b3e31 | 3812 | of the work (in the case of addition/subtraction, less for |
58cde26e JH |
3813 | multiplication/division). If $y is very small compared to $x, the form |
3814 | $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes | |
3815 | more time then the actual addition. | |
3816 | ||
b22b3e31 | 3817 | With a technique called copy-on-write, the cost of copying with overload could |
394e6ffb JH |
3818 | be minimized or even completely avoided. A test implementation of COW did show |
3819 | performance gains for overloaded math, but introduced a performance loss due | |
091c87b1 T |
3820 | to a constant overhead for all other operatons. So Math::BigInt does currently |
3821 | not COW. | |
394e6ffb | 3822 | |
091c87b1 T |
3823 | The rewritten version of this module (vs. v0.01) is slower on certain |
3824 | operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it | |
3825 | does now more work and handles much more cases. The time spent in these | |
3826 | operations is usually gained in the other math operations so that code on | |
3827 | the average should get (much) faster. If they don't, please contact the author. | |
58cde26e | 3828 | |
394e6ffb | 3829 | Some operations may be slower for small numbers, but are significantly faster |
091c87b1 T |
3830 | for big numbers. Other operations are now constant (O(1), like C<bneg()>, |
3831 | C<babs()> etc), instead of O(N) and thus nearly always take much less time. | |
3832 | These optimizations were done on purpose. | |
58cde26e | 3833 | |
574bacfe JH |
3834 | If you find the Calc module to slow, try to install any of the replacement |
3835 | modules and see if they help you. | |
b3ac6de7 | 3836 | |
574bacfe | 3837 | =head2 Alternative math libraries |
0716bf9b JH |
3838 | |
3839 | You can use an alternative library to drive Math::BigInt via: | |
3840 | ||
3841 | use Math::BigInt lib => 'Module'; | |
3842 | ||
394e6ffb | 3843 | See L<MATH LIBRARY> for more information. |
0716bf9b | 3844 | |
394e6ffb | 3845 | For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>. |
574bacfe | 3846 | |
b3abae2a JH |
3847 | =head2 SUBCLASSING |
3848 | ||
3849 | =head1 Subclassing Math::BigInt | |
3850 | ||
3851 | The basic design of Math::BigInt allows simple subclasses with very little | |
3852 | work, as long as a few simple rules are followed: | |
3853 | ||
3854 | =over 2 | |
3855 | ||
3856 | =item * | |
3857 | ||
3858 | The public API must remain consistent, i.e. if a sub-class is overloading | |
3859 | addition, the sub-class must use the same name, in this case badd(). The | |
3860 | reason for this is that Math::BigInt is optimized to call the object methods | |
3861 | directly. | |
3862 | ||
3863 | =item * | |
3864 | ||
3865 | The private object hash keys like C<$x->{sign}> may not be changed, but | |
3866 | additional keys can be added, like C<$x->{_custom}>. | |
3867 | ||
3868 | =item * | |
3869 | ||
3870 | Accessor functions are available for all existing object hash keys and should | |
3871 | be used instead of directly accessing the internal hash keys. The reason for | |
3872 | this is that Math::BigInt itself has a pluggable interface which permits it | |
3873 | to support different storage methods. | |
3874 | ||
3875 | =back | |
3876 | ||
3877 | More complex sub-classes may have to replicate more of the logic internal of | |
3878 | Math::BigInt if they need to change more basic behaviors. A subclass that | |
3879 | needs to merely change the output only needs to overload C<bstr()>. | |
3880 | ||
3881 | All other object methods and overloaded functions can be directly inherited | |
3882 | from the parent class. | |
3883 | ||
3884 | At the very minimum, any subclass will need to provide it's own C<new()> and can | |
3885 | store additional hash keys in the object. There are also some package globals | |
3886 | that must be defined, e.g.: | |
3887 | ||
3888 | # Globals | |
3889 | $accuracy = undef; | |
3890 | $precision = -2; # round to 2 decimal places | |
3891 | $round_mode = 'even'; | |
3892 | $div_scale = 40; | |
3893 | ||
3894 | Additionally, you might want to provide the following two globals to allow | |
3895 | auto-upgrading and auto-downgrading to work correctly: | |
3896 | ||
3897 | $upgrade = undef; | |
3898 | $downgrade = undef; | |
3899 | ||
3900 | This allows Math::BigInt to correctly retrieve package globals from the | |
3901 | subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or | |
3902 | t/Math/BigFloat/SubClass.pm completely functional subclass examples. | |
3903 | ||
3904 | Don't forget to | |
3905 | ||
3906 | use overload; | |
3907 | ||
3908 | in your subclass to automatically inherit the overloading from the parent. If | |
3909 | you like, you can change part of the overloading, look at Math::String for an | |
3910 | example. | |
3911 | ||
3912 | =head1 UPGRADING | |
3913 | ||
3914 | When used like this: | |
3915 | ||
3916 | use Math::BigInt upgrade => 'Foo::Bar'; | |
3917 | ||
3918 | certain operations will 'upgrade' their calculation and thus the result to | |
3919 | the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: | |
3920 | ||
3921 | use Math::BigInt upgrade => 'Math::BigFloat'; | |
3922 | ||
3923 | As a shortcut, you can use the module C<bignum>: | |
3924 | ||
3925 | use bignum; | |
3926 | ||
3927 | Also good for oneliners: | |
3928 | ||
3929 | perl -Mbignum -le 'print 2 ** 255' | |
3930 | ||
3931 | This makes it possible to mix arguments of different classes (as in 2.5 + 2) | |
3932 | as well es preserve accuracy (as in sqrt(3)). | |
3933 | ||
3934 | Beware: This feature is not fully implemented yet. | |
3935 | ||
3936 | =head2 Auto-upgrade | |
3937 | ||
3938 | The following methods upgrade themselves unconditionally; that is if upgrade | |
3939 | is in effect, they will always hand up their work: | |
3940 | ||
3941 | =over 2 | |
3942 | ||
3943 | =item bsqrt() | |
3944 | ||
3945 | =item div() | |
3946 | ||
3947 | =item blog() | |
3948 | ||
3949 | =back | |
3950 | ||
3951 | Beware: This list is not complete. | |
3952 | ||
3953 | All other methods upgrade themselves only when one (or all) of their | |
3954 | arguments are of the class mentioned in $upgrade (This might change in later | |
3955 | versions to a more sophisticated scheme): | |
3956 | ||
a5f75d66 AD |
3957 | =head1 BUGS |
3958 | ||
58cde26e JH |
3959 | =over 2 |
3960 | ||
990fb837 RGS |
3961 | =item broot() does not work |
3962 | ||
3963 | The broot() function in BigInt may only work for small values. This will be | |
3964 | fixed in a later version. | |
3965 | ||
574bacfe | 3966 | =item Out of Memory! |
58cde26e JH |
3967 | |
3968 | Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and | |
3969 | C<eval()> in your code will crash with "Out of memory". This is probably an | |
3970 | overload/exporter bug. You can workaround by not having C<eval()> | |
574bacfe JH |
3971 | and ':constant' at the same time or upgrade your Perl to a newer version. |
3972 | ||
3973 | =item Fails to load Calc on Perl prior 5.6.0 | |
3974 | ||
3975 | Since eval(' use ...') can not be used in conjunction with ':constant', BigInt | |
3976 | will fall back to eval { require ... } when loading the math lib on Perls | |
3977 | prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on | |
3978 | filesystems using a different seperator. | |
58cde26e JH |
3979 | |
3980 | =back | |
3981 | ||
3982 | =head1 CAVEATS | |
3983 | ||
3984 | Some things might not work as you expect them. Below is documented what is | |
3985 | known to be troublesome: | |
3986 | ||
3987 | =over 1 | |
3988 | ||
091c87b1 | 3989 | =item bstr(), bsstr() and 'cmp' |
58cde26e | 3990 | |
091c87b1 T |
3991 | Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now |
3992 | drop the leading '+'. The old code would return '+3', the new returns '3'. | |
3993 | This is to be consistent with Perl and to make C<cmp> (especially with | |
3994 | overloading) to work as you expect. It also solves problems with C<Test.pm>, | |
3995 | because it's C<ok()> uses 'eq' internally. | |
58cde26e | 3996 | |
091c87b1 T |
3997 | Mark Biggar said, when asked about to drop the '+' altogether, or make only |
3998 | C<cmp> work: | |
58cde26e JH |
3999 | |
4000 | I agree (with the first alternative), don't add the '+' on positive | |
4001 | numbers. It's not as important anymore with the new internal | |
4002 | form for numbers. It made doing things like abs and neg easier, | |
4003 | but those have to be done differently now anyway. | |
4004 | ||
4005 | So, the following examples will now work all as expected: | |
4006 | ||
4007 | use Test; | |
4008 | BEGIN { plan tests => 1 } | |
4009 | use Math::BigInt; | |
4010 | ||
4011 | my $x = new Math::BigInt 3*3; | |
4012 | my $y = new Math::BigInt 3*3; | |
4013 | ||
4014 | ok ($x,3*3); | |
4015 | print "$x eq 9" if $x eq $y; | |
4016 | print "$x eq 9" if $x eq '9'; | |
4017 | print "$x eq 9" if $x eq 3*3; | |
4018 | ||
4019 | Additionally, the following still works: | |
4020 | ||
4021 | print "$x == 9" if $x == $y; | |
4022 | print "$x == 9" if $x == 9; | |
4023 | print "$x == 9" if $x == 3*3; | |
4024 | ||
4025 | There is now a C<bsstr()> method to get the string in scientific notation aka | |
4026 | C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() | |
4027 | for comparisation, but Perl will represent some numbers as 100 and others | |
091c87b1 T |
4028 | as 1e+308. If in doubt, convert both arguments to Math::BigInt before |
4029 | comparing them as strings: | |
58cde26e JH |
4030 | |
4031 | use Test; | |
4032 | BEGIN { plan tests => 3 } | |
4033 | use Math::BigInt; | |
4034 | ||
4035 | $x = Math::BigInt->new('1e56'); $y = 1e56; | |
4036 | ok ($x,$y); # will fail | |
4037 | ok ($x->bsstr(),$y); # okay | |
4038 | $y = Math::BigInt->new($y); | |
4039 | ok ($x,$y); # okay | |
4040 | ||
091c87b1 T |
4041 | Alternatively, simple use C<< <=> >> for comparisations, this will get it |
4042 | always right. There is not yet a way to get a number automatically represented | |
4043 | as a string that matches exactly the way Perl represents it. | |
574bacfe | 4044 | |
58cde26e JH |
4045 | =item int() |
4046 | ||
4047 | C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a | |
4048 | Perl scalar: | |
4049 | ||
4050 | $x = Math::BigInt->new(123); | |
4051 | $y = int($x); # BigInt 123 | |
4052 | $x = Math::BigFloat->new(123.45); | |
4053 | $y = int($x); # BigInt 123 | |
4054 | ||
4055 | In all Perl versions you can use C<as_number()> for the same effect: | |
4056 | ||
4057 | $x = Math::BigFloat->new(123.45); | |
4058 | $y = $x->as_number(); # BigInt 123 | |
4059 | ||
4060 | This also works for other subclasses, like Math::String. | |
4061 | ||
574bacfe JH |
4062 | It is yet unlcear whether overloaded int() should return a scalar or a BigInt. |
4063 | ||
dccbb853 | 4064 | =item length |
58cde26e JH |
4065 | |
4066 | The following will probably not do what you expect: | |
4067 | ||
bd05a461 JH |
4068 | $c = Math::BigInt->new(123); |
4069 | print $c->length(),"\n"; # prints 30 | |
4070 | ||
4071 | It prints both the number of digits in the number and in the fraction part | |
4072 | since print calls C<length()> in list context. Use something like: | |
4073 | ||
4074 | print scalar $c->length(),"\n"; # prints 3 | |
4075 | ||
4076 | =item bdiv | |
4077 | ||
4078 | The following will probably not do what you expect: | |
4079 | ||
58cde26e JH |
4080 | print $c->bdiv(10000),"\n"; |
4081 | ||
dccbb853 | 4082 | It prints both quotient and remainder since print calls C<bdiv()> in list |
58cde26e JH |
4083 | context. Also, C<bdiv()> will modify $c, so be carefull. You probably want |
4084 | to use | |
4085 | ||
4086 | print $c / 10000,"\n"; | |
4087 | print scalar $c->bdiv(10000),"\n"; # or if you want to modify $c | |
4088 | ||
4089 | instead. | |
4090 | ||
4091 | The quotient is always the greatest integer less than or equal to the | |
4092 | real-valued quotient of the two operands, and the remainder (when it is | |
4093 | nonzero) always has the same sign as the second operand; so, for | |
4094 | example, | |
4095 | ||
dccbb853 JH |
4096 | 1 / 4 => ( 0, 1) |
4097 | 1 / -4 => (-1,-3) | |
4098 | -3 / 4 => (-1, 1) | |
4099 | -3 / -4 => ( 0,-3) | |
4100 | -11 / 2 => (-5,1) | |
4101 | 11 /-2 => (-5,-1) | |
58cde26e JH |
4102 | |
4103 | As a consequence, the behavior of the operator % agrees with the | |
4104 | behavior of Perl's built-in % operator (as documented in the perlop | |
4105 | manpage), and the equation | |
4106 | ||
4107 | $x == ($x / $y) * $y + ($x % $y) | |
4108 | ||
4109 | holds true for any $x and $y, which justifies calling the two return | |
dccbb853 JH |
4110 | values of bdiv() the quotient and remainder. The only exception to this rule |
4111 | are when $y == 0 and $x is negative, then the remainder will also be | |
4112 | negative. See below under "infinity handling" for the reasoning behing this. | |
58cde26e JH |
4113 | |
4114 | Perl's 'use integer;' changes the behaviour of % and / for scalars, but will | |
4115 | not change BigInt's way to do things. This is because under 'use integer' Perl | |
4116 | will do what the underlying C thinks is right and this is different for each | |
4117 | system. If you need BigInt's behaving exactly like Perl's 'use integer', bug | |
4118 | the author to implement it ;) | |
4119 | ||
dccbb853 JH |
4120 | =item infinity handling |
4121 | ||
4122 | Here are some examples that explain the reasons why certain results occur while | |
4123 | handling infinity: | |
4124 | ||
4125 | The following table shows the result of the division and the remainder, so that | |
4126 | the equation above holds true. Some "ordinary" cases are strewn in to show more | |
4127 | clearly the reasoning: | |
4128 | ||
4129 | A / B = C, R so that C * B + R = A | |
4130 | ========================================================= | |
4131 | 5 / 8 = 0, 5 0 * 8 + 5 = 5 | |
4132 | 0 / 8 = 0, 0 0 * 8 + 0 = 0 | |
4133 | 0 / inf = 0, 0 0 * inf + 0 = 0 | |
4134 | 0 /-inf = 0, 0 0 * -inf + 0 = 0 | |
4135 | 5 / inf = 0, 5 0 * inf + 5 = 5 | |
4136 | 5 /-inf = 0, 5 0 * -inf + 5 = 5 | |
4137 | -5/ inf = 0, -5 0 * inf + -5 = -5 | |
4138 | -5/-inf = 0, -5 0 * -inf + -5 = -5 | |
4139 | inf/ 5 = inf, 0 inf * 5 + 0 = inf | |
4140 | -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf | |
4141 | inf/ -5 = -inf, 0 -inf * -5 + 0 = inf | |
4142 | -inf/ -5 = inf, 0 inf * -5 + 0 = -inf | |
4143 | 5/ 5 = 1, 0 1 * 5 + 0 = 5 | |
4144 | -5/ -5 = 1, 0 1 * -5 + 0 = -5 | |
4145 | inf/ inf = 1, 0 1 * inf + 0 = inf | |
4146 | -inf/-inf = 1, 0 1 * -inf + 0 = -inf | |
4147 | inf/-inf = -1, 0 -1 * -inf + 0 = inf | |
4148 | -inf/ inf = -1, 0 1 * -inf + 0 = -inf | |
4149 | 8/ 0 = inf, 8 inf * 0 + 8 = 8 | |
4150 | inf/ 0 = inf, inf inf * 0 + inf = inf | |
4151 | 0/ 0 = NaN | |
4152 | ||
4153 | These cases below violate the "remainder has the sign of the second of the two | |
4154 | arguments", since they wouldn't match up otherwise. | |
4155 | ||
4156 | A / B = C, R so that C * B + R = A | |
4157 | ======================================================== | |
4158 | -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf | |
4159 | -8/ 0 = -inf, -8 -inf * 0 + 8 = -8 | |
4160 | ||
58cde26e JH |
4161 | =item Modifying and = |
4162 | ||
4163 | Beware of: | |
4164 | ||
4165 | $x = Math::BigFloat->new(5); | |
4166 | $y = $x; | |
4167 | ||
4168 | It will not do what you think, e.g. making a copy of $x. Instead it just makes | |
4169 | a second reference to the B<same> object and stores it in $y. Thus anything | |
17baacb7 JH |
4170 | that modifies $x (except overloaded operators) will modify $y, and vice versa. |
4171 | Or in other words, C<=> is only safe if you modify your BigInts only via | |
4172 | overloaded math. As soon as you use a method call it breaks: | |
58cde26e JH |
4173 | |
4174 | $x->bmul(2); | |
4175 | print "$x, $y\n"; # prints '10, 10' | |
4176 | ||
4177 | If you want a true copy of $x, use: | |
4178 | ||
4179 | $y = $x->copy(); | |
4180 | ||
17baacb7 JH |
4181 | You can also chain the calls like this, this will make first a copy and then |
4182 | multiply it by 2: | |
4183 | ||
4184 | $y = $x->copy()->bmul(2); | |
4185 | ||
b22b3e31 | 4186 | See also the documentation for overload.pm regarding C<=>. |
58cde26e JH |
4187 | |
4188 | =item bpow | |
4189 | ||
4190 | C<bpow()> (and the rounding functions) now modifies the first argument and | |
574bacfe | 4191 | returns it, unlike the old code which left it alone and only returned the |
58cde26e JH |
4192 | result. This is to be consistent with C<badd()> etc. The first three will |
4193 | modify $x, the last one won't: | |
4194 | ||
4195 | print bpow($x,$i),"\n"; # modify $x | |
4196 | print $x->bpow($i),"\n"; # ditto | |
4197 | print $x **= $i,"\n"; # the same | |
4198 | print $x ** $i,"\n"; # leave $x alone | |
4199 | ||
4200 | The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. | |
4201 | ||
4202 | =item Overloading -$x | |
4203 | ||
4204 | The following: | |
4205 | ||
4206 | $x = -$x; | |
4207 | ||
4208 | is slower than | |
4209 | ||
4210 | $x->bneg(); | |
4211 | ||
4212 | since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant | |
4213 | needs to preserve $x since it does not know that it later will get overwritten. | |
0716bf9b | 4214 | This makes a copy of $x and takes O(N), but $x->bneg() is O(1). |
58cde26e | 4215 | |
394e6ffb JH |
4216 | With Copy-On-Write, this issue would be gone, but C-o-W is not implemented |
4217 | since it is slower for all other things. | |
58cde26e JH |
4218 | |
4219 | =item Mixing different object types | |
4220 | ||
4221 | In Perl you will get a floating point value if you do one of the following: | |
4222 | ||
4223 | $float = 5.0 + 2; | |
4224 | $float = 2 + 5.0; | |
4225 | $float = 5 / 2; | |
4226 | ||
4227 | With overloaded math, only the first two variants will result in a BigFloat: | |
4228 | ||
4229 | use Math::BigInt; | |
4230 | use Math::BigFloat; | |
4231 | ||
4232 | $mbf = Math::BigFloat->new(5); | |
4233 | $mbi2 = Math::BigInteger->new(5); | |
4234 | $mbi = Math::BigInteger->new(2); | |
4235 | ||
4236 | # what actually gets called: | |
4237 | $float = $mbf + $mbi; # $mbf->badd() | |
4238 | $float = $mbf / $mbi; # $mbf->bdiv() | |
4239 | $integer = $mbi + $mbf; # $mbi->badd() | |
4240 | $integer = $mbi2 / $mbi; # $mbi2->bdiv() | |
4241 | $integer = $mbi2 / $mbf; # $mbi2->bdiv() | |
4242 | ||
4243 | This is because math with overloaded operators follows the first (dominating) | |
394e6ffb | 4244 | operand, and the operation of that is called and returns thus the result. So, |
58cde26e JH |
4245 | Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether |
4246 | the result should be a Math::BigFloat or the second operant is one. | |
4247 | ||
4248 | To get a Math::BigFloat you either need to call the operation manually, | |
4249 | make sure the operands are already of the proper type or casted to that type | |
4250 | via Math::BigFloat->new(): | |
4251 | ||
4252 | $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 | |
4253 | ||
4254 | Beware of simple "casting" the entire expression, this would only convert | |
4255 | the already computed result: | |
4256 | ||
4257 | $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong! | |
4258 | ||
0716bf9b | 4259 | Beware also of the order of more complicated expressions like: |
58cde26e JH |
4260 | |
4261 | $integer = ($mbi2 + $mbi) / $mbf; # int / float => int | |
4262 | $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto | |
4263 | ||
4264 | If in doubt, break the expression into simpler terms, or cast all operands | |
4265 | to the desired resulting type. | |
4266 | ||
4267 | Scalar values are a bit different, since: | |
4268 | ||
4269 | $float = 2 + $mbf; | |
4270 | $float = $mbf + 2; | |
4271 | ||
4272 | will both result in the proper type due to the way the overloaded math works. | |
4273 | ||
4274 | This section also applies to other overloaded math packages, like Math::String. | |
4275 | ||
990fb837 RGS |
4276 | One solution to you problem might be autoupgrading|upgrading. See the |
4277 | pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this. | |
b3abae2a | 4278 | |
58cde26e JH |
4279 | =item bsqrt() |
4280 | ||
394e6ffb | 4281 | C<bsqrt()> works only good if the result is a big integer, e.g. the square |
58cde26e | 4282 | root of 144 is 12, but from 12 the square root is 3, regardless of rounding |
990fb837 | 4283 | mode. The reason is that the result is always truncated to an integer. |
58cde26e JH |
4284 | |
4285 | If you want a better approximation of the square root, then use: | |
4286 | ||
4287 | $x = Math::BigFloat->new(12); | |
394e6ffb | 4288 | Math::BigFloat->precision(0); |
58cde26e JH |
4289 | Math::BigFloat->round_mode('even'); |
4290 | print $x->copy->bsqrt(),"\n"; # 4 | |
4291 | ||
394e6ffb | 4292 | Math::BigFloat->precision(2); |
58cde26e JH |
4293 | print $x->bsqrt(),"\n"; # 3.46 |
4294 | print $x->bsqrt(3),"\n"; # 3.464 | |
4295 | ||
b3abae2a JH |
4296 | =item brsft() |
4297 | ||
4298 | For negative numbers in base see also L<brsft|brsft>. | |
4299 | ||
58cde26e JH |
4300 | =back |
4301 | ||
4302 | =head1 LICENSE | |
4303 | ||
4304 | This program is free software; you may redistribute it and/or modify it under | |
4305 | the same terms as Perl itself. | |
a5f75d66 | 4306 | |
0716bf9b JH |
4307 | =head1 SEE ALSO |
4308 | ||
990fb837 RGS |
4309 | L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as |
4310 | L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
4311 | ||
4312 | The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest | |
4313 | because they solve the autoupgrading/downgrading issue, at least partly. | |
0716bf9b | 4314 | |
027dc388 JH |
4315 | The package at |
4316 | L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains | |
4317 | more documentation including a full version history, testcases, empty | |
4318 | subclass files and benchmarks. | |
574bacfe | 4319 | |
58cde26e | 4320 | =head1 AUTHORS |
a5f75d66 | 4321 | |
58cde26e | 4322 | Original code by Mark Biggar, overloaded interface by Ilya Zakharevich. |
ef9466ea T |
4323 | Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2003 |
4324 | and still at it in 2004. | |
990fb837 RGS |
4325 | |
4326 | Many people contributed in one or more ways to the final beast, see the file | |
4327 | CREDITS for an (uncomplete) list. If you miss your name, please drop me a | |
4328 | mail. Thank you! | |
a5f75d66 AD |
4329 | |
4330 | =cut |